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FREE-HAND   DRAWING 

LIGHT  AND  SHADE 

AND 

FREE-HAND    PERSPECTIVE 

FOR   THE   USE  OF 

Art  students  and  Teachers 

BY 

ANSON    K.   CROSS 

Instructor  in  the  Massachtsetts  Normal  Art  School  and  in  the  School 
OF  Drawing  and  Painting,  Museum  of  Fine  Arts,  Boston 

ILLUSTRATED   BY   32   PLATES 


BOSTON 

PUBLISHED  BY  THE  AUTHOR 

1S92 


CorvRiciiT,  1892, 
By  ANSON   K.  CROSS. 


All  Rights  Reserved. 


Typography  by  J.  S.  Cushwo  &  Co.,  Boston. 


JIL 


TO 

MY    FRIEND   AND    FIRST   TEACHER 
Eobrrt  ?:H.  Fonnolj 

I     INSCRIBE    THIS     BOOK 

IN    RECOGNITION 

OF  HIS  EFFORTS  TO  ADVANCE 

SERIOUS   AND   CONSCIENTIOUS 

STUDY   OF   NATURE 


IK 


PREFACE. 


The  notes  on  Model  Drawing,  forming  the  body  of  this 
book,  were  prepared  for  the  use  of  the  students  of  the  Mas- 
sachusetts Normal  Art  School.  They  were  printed  with- 
out illustrations,  as  explanations  of  the  drawings  given  in 
the  course  of  lectures  on  this  subject,  and  will  be  of 
little  assistance  to  those  not  taking  the  lectures.  Having 
been  requested  for  the  book  by  persons  not  students  of 
the  school,  and  realizing  that  drawing  is  often  poorly 
taught,  especially  in  our  public  schools,  and  being  unable 
to  recommend  a  book  which  treats  the  subject  simply 
and  presents  artistic  methods  of  work,  I  concluded  to 
rewrite  the  notes,  adapting  them  to  general  use,  and 
meeting,  as  far  as  possible,  the  demand  for  a  text-book 
on  the  principles  of  free-hand  drawing. 

The  book  is  intended  especially  for  teachers,  and  at 
first  glance  the  artist  may  think  it  considers  more  theory 
than  is  necessary.  No  one  can  be  more  strongly  con- 
vinced than  I,  of  the  folly  of  teaching  and  depending 
upon  theory  alone.     I  believe  that  theory  is  of  use  only 


vi  PREFACE. 

to  the  artist  who  can  draw  without  it.  To  such  a  per- 
son and  to  the  teacher,  theory  may  be  of  great  assist- 
ance. The  artist  who  should  depend  upon  theory 
instead  of  upon  his  eyes,  would  certainly  be  ver)-  unwise, 
and  would  probably  produce  unsatisfactory  work.  If  his 
work  consisted  simply  in  drawing  from  Nature,  and  from 
subjects  before  him  exactly  as  they  are  to  be  repre- 
sented, he  would  have  little  need  of  theory,  and  could 
safely  depend  upon  his  eyes ;  but  the  artist  often  has 
to  design  and  draw  without  a  subject  before  him,  and 
for  this  work  he  must  depend  upon  his  knowledge.  If 
this  has  been  arranged  under  a  few  simple  rules  which 
he  has  discovered  while  drawing  from  Nature,  he  will 
draw  with  more  freedom  and  for  greater  accuracy  than 
when  without  these  helps. 

If  his  mind  is  so  constructed  that  he  cannot  discover 
and  apply  the  few  rules  necessary  for  this  work,  it  is 
quite  likely  that  his  time  will  be  more  profitably  spent 
in  some  other  direction ;  for  the  rules  of  perspective 
which  the  artist  requires  are  so  simple  as  to  be  easily 
given  in  a  few  sentences.  From  the  standpoint  of  the 
artist,  then,  there  may  be  more  theory  than  is  needed, 
but  the  teacher  of  much  experience  will  not  find  this 
true. 

Every  teacher  has  found  the  bright,  thoughtful  student 
who  has  asked  questions  of  which  the  teacher  has  never 
thought.     Nearly  all  the  points  considered  in  these  notes 


PREFACE.  vii 

have  been  suggested  by  such  questions,  which  have  been 
referred  to  me.  It  is  impossible  to  furnish  answers  to 
all  the  questions  which  the  teacher  is  likely  to  be  asked, 
but  the  main  points  can  be  covered,  and  these  under- 
stood, other  (luestions  depending  upon  them  can  be 
readily  met. 

Though  intended  for  the  teacher  and  student,  the 
subject-matter  is  to  a  greater  or  less  extent  interesting  to 
the  artist,  the  illustrator,  and  others  who  may  not  have 
the  knowledge  of  Projection  and  Scientific  Persjiective 
necessary  to  follow  some  of  the  problems  considered. 
'J'he  i)roblems  requiring  this  knowledge  are  more  impor- 
tant to  the  teacher  than  to  tlie  artist,  and  it  is  hoped 
that  the  average  art  student  may  find  the  simpler  prob- 
lems suited  to  his  capacity  and  his  needs,  aiul  that  those 
not  interested  in  the  scientific  discussions  will  study  the 
parts  intended  for  them. 

The  teacher  may  feel  inclined  to  criticise  the  way  in 
which  the  free-hand  part  of  the  subject  is  presented.  He 
may  desire  a  rule  as  to  which  line  to  draw  first,  which 
second,  etc.  He  may  not  wish  to  cultivate  his  feeling  to 
sucli  an  extent  as  to  cast  aside  conventional  methods  of 
working.  He  may  upon  consideration  acknowledge  the 
methods  advised  to  be  more  artistic,  but  he  may  say 
that  they  are  harder  to  teach.  There  is  no  question  but 
that  artistic  feeling  and  correct  taste  are  difficult  to 
obtain,  but  surely  this  is  no  reason  why  we  should  not 


viii  PREFACE. 

cultivate  the  small  amount  of  taste  which  the  students 
may  possess,  no  reason  for  choosing  conventional  and 
mechanical  methods  which  must  destroy  artistic  feeling. 

An  artistic  method  is  difficult  to  teach  to  students  who 
have  been  taught  an  inartistic  one,  and  the  change  will  > 
involve  a  stniggle  on  the  part  of  both  pupil  and  teacher ; 
but  I  do  not  admit  that  it  is  more  difficult  to  start  right 
than  to  start  wrong,  and  the  objections  of  those  who 
have  to  change  old  methods  will  last  only  as  long  as 
they  refuse  to  change.  I  believe  that  the  easiest  and  the 
best  time  to  train  the  eye  to  see  is  in  the  beginning, 
when  the  mind  has  not  been  so  developed  as  to  perform 
nearly  all  the  duties  of  the  eye.  If  there  were  any  way 
by  which  less  knowledge  of  the  things  seen  could  be 
awakened,  it  would  be  unnecessary  for  the  student  to 
spend  many  years  of  severe  labor  to  enable  himself  to 
see,  and  not  to  reason  the  appearance  of  Nature  ;  but 
until  the  training  of  the  mind  to  accept  the  story  of  the 
eye  is  made  as  complete  as,  and  begins  with,  the  training 
of  the  mind  concerning  facts,  the  art  student  will  in 
truth  find  that  "  Art  is  long." 

There  is  no  good  reason  for  postponing  this  training 
until  the  student  decides  to  make  Art  his  profession,  and 
when  it  is  realized  that  the  teacher  in  charge  of  art  edu- 
cation in  the  public  schools  has  a  most  important  posi- 
tion, the  first  step  in  advance  will  have  been  made. 
Ability  to  talk  well  and  intelligently  of  general  matters, 


PREFACE.  ix 

and  even  of  art  as  presented  by  various  writers,  does  not 
constitute  this  special  fitness ;  neither  does  the  ability  to 
draw  pretty  things  upon  the  blackboard,  nor  to  explain 
the  course  as  arranged  in  a  set  of  text-books  ;  and  even 
the  faculty  of  planning  and  carrying  out  a  course  so  as 
to  produce  an  interesting  exhibition  of  drawings,  fancy 
work,  manual  training,  etc.,  is  not  enough.  All  these 
things  are  important,  but  of  greater  importance  is  per- 
sonal artistic  feeling  and  practical  ability  in  art,  involving 
more  study  than  most  who  are  teaching  in  the  public 
schools  have  been  able  to  give.  Without  this  training, 
which  alone  can  enable  one  to  justly  realize  the  end  of 
his  teaching  and  thus  to  work  from  the  first  for  this  end, 
the  instruction  given  must  be  unnecessary,  mechanical, 
illogical,  and  harmful. 

I  do  not  wish  to  disparage  the  valuable  results  which 
have  been  accomplished,  nor  to  criticise  the  teachers 
who  have  worked  so  foithfully  in  this  field.  I  wish  sim- 
ply to  encourage  those  now  in  the  work  to  look  for  its 
artistic  qualities  as  much  as  possible,  and  to  advise  those 
intending  to  take  up  the  study  to  obtain  good  art  training, 
and  not  to  accept  as  a  good  reason  for  proceeding  in  a 
certain  way  the  fact  that  all  authorities  of  the  past  have 
done  thus.  The  influence  of  the  honest  impressionist 
is  being  felt.  We  are  beginning  to  use  our  own  eyes 
instead  of  those  of  other  people,  who  in  like  manner  have 
depended  upon  others,  and  the  time  is  at  hand  when  in 


PREFACE. 


spite  of  the  present  ridicule  of"  those  who  have  never 
learned  to  see,  the  honest  student  of  appearances  will  be 
appreciated,  and  those  who  ridicule  will  be  forced  to 
study  or  to  step  into  the  background. 


CHAPTER    I. 
Training  of  the  Art  Student. 

Much  has  been  said  and  written  concerning  this  sub- 
ject, but  there  seems  to  be  no  more  unanimity  of  opinion 
than  in  the  past,  I  should  hesitate  to  say  anything  upon 
this  point,  if  the  subject  of  art  instruction  could  be  con- 
sidered in  part ;  but  this  is  impossible.  The  influence  of 
the  higher  art  instruction  is  felt  through  all  the  earliest 
attempts  in  this  direction,  and  the  matter  of  art  instruc- 
tion in  the  public  schools  is  in  its  present  chaotic  con- 
dition largely  through  the  contradictory  teachings  of 
many  advanced  art  schools. 

I  am  aware  that  my  opinions  are  very  different  from 
those  of  some  who  have  established  reputations  as  writers 
and  teachers,  but  I  also  know  that  others  will  agree  with 
me.  The  variety  of  opinions  upon  this  subject  is  due  to 
the  different  individualities  and  to  the  lines  of  training 
pursued.  The  average  person  changes  fliith  in  religion, 
Art,  or  any  subject  long  considered  very  rarely.  Preju- 
dice and  unquestioning  faith  in  the  doctrines  in  which 

I 


2  FREE-HAND  DRAWING. 

we  have  been  educated   prevent   even  consideration  of 
the  opinions  of  other  people. 

The  abihty  to  think  and  act  independently  is  possessed 
by  the  few  who  lead.  Thus  it  is  that  we  recognize  in  the 
work  of  an  artist  the  technit^ue  of  the  teacher  with  whom 
he  has  studied,  and  find  him  free^uently  unable  to  see 
merit  except  in  his  favorite  school ;  and  some  are  unable 
to  separate  the  result  from  the  way  by  which  it  was  pro- 
duced, the  method  being  of  greater  importance  than  the 
result. 

The  tendency  in  this  direction  increases  as  the  ability 
decreases,  and  is  strongest  among  those  who  direct  art 
instruction  in  the  public  schools.  This  is  the  result  of 
teachers,  who  have  given  great  attention  to  the  best 
methods  of  teaching  the  ordinary  branches,  attempting 
to  teach  art  when  they  know  nothing  of  it,  and  naturally 
arises  from  the  necessity  which  exists  in  most  places  for 
the  regular  teachers  giving  the  lessons  in  drawing.  I 
will  consider  this  work  by  itself,  but  I  wish  now  to 
express  the  impossibility  of  formulating  systematized 
schemes  arbitrarily  fixing  details  of  art  work,  and  rules 
by  which  it  is  to  be  judged  as  good  or  bad. 

I  have  known  of  teachers  who  have  told  their  students 
that  all  methods  but  a  certain  way  of  working  or  using  a 
medium  were  out  of  date,  and  that  drawings  made  in 
these  ways  were  necessarily  bad.  I  have  seen  the 
attempt  to  produce  work  in  accordance  with  some  such 


TRAINING    OF   THE  ART  STUDENT.  3 

l)lan  result  in  atrociously  bad  drawings,  which  nevertheless 
were  to  be  admired  because  done  according  to  the  latest 
and  only  approved  method.  Some^  for  instance,  now  say 
that  a  charcoal  drawing  must  be  made  entirely  with  the . 
poijlLof  the  charcoal,  and  that  if  the  drawing  shows  any 
blending,  it  is  not  good.  Such  a  statement  results  only 
from  the  ignorance  which  looks  at  the  paper  and  char- 
coal instead  of  for  the  effect  or  the  impression  the  draw- 
ing is  intended  to  convey. 

The  problem  for  the  art  student  to  master  is  drawing, 
—  it  is  drawing  whether  he  uses  the  pencil  in  an  outline 
sketch,  the  charcoal  in  a  shaded  sketch,  or  the  brush 
and  color.  Though  new  colors  may  be  discovered,  the 
problem  is  practically  what  it  has  been  for  hundreds  of 
years,  during  which  time  almost  all  ways  and  means  of 
producing  a  drawing  have  been  tried  and  used  success- 
fully by  those  who  have  practised  art.  The  strong  artists 
of  the  past  did  not  confine  themselves  to  one  medium  or 
to  one  way  of  using  it.  They  worked  with  pencil,  crayon, 
pen  and  ink,  chalk,  water  color,  oil,  and  other  mediums, 
apparently  often  using  that  which  was  handiest.  Their 
aim  was  not  the  way  of  using  the  medium,  but  the  ex- 
pression of  an  idea,  and  this  must  be  the  only  end  worthy 
of  the  best  effort  of  the  artist. 

Too  much  importance  is  laid  on  technique  and  the  way 
the  story  is  told.  It  is  even  said  that  in  looking  at  a 
picture,  we  should  first  see  how  it  is  painted,  as  if  the 


\ 


4  FREE-HAND  DRAWING. 

kind  of  canvas,  the  thickness  or  thinness  of  the  paint,  and 
how  it  is  appHed,  concerns  the  public.  As  well  might  we 
say  that  we  must  analyze  the  peach  to  decide  whether  or 
no  we  like  its  flavor ;  or  formulate  a  theory  of  color  to 
decide  if  the  color  of  its  skin  is  agreeable ;  or  analyze 
the  sentences  of  an  orator  before  we  can  permit  ourselves 
to  be  moved  by  his  eloquence.  The  question  of  tech- 
nique  should  be  accorded  the  importance  which  it 
deserves,  and  it  deser\-es  very  little.  If  a  picture  tells  its 
story  well,  and  is  pleasing  in  color  and  sentiment,  it  must 
be  good  whether  painted  with  much  labor  or  quickly, 
whether  the  pamt  is  thick  or  thin,  rough  or  smooth. 
When  the  public  realizes  that  it  is  not  methods  but  results 
which  constitute  art,  a  great  advance  will  have  been 
made. 

The  question  of  how  the  picture  is  painted  should  con- 
cern only  the  artist  and  the  advanced,  student,  for  they 
are  interested  in  its  practical  construction  as  a  builder  is 
interested  in  that  of  the  houses  which  he  sees. 

To  the  student,  a  study  of  the  ways  in  which  other 
painters  have  secured  results  serves  as  a  guide  and  cor- 
rective. But  it  is  important  to  observe  that  strong  painters 
work  in  many  different  ways,  and  pictures  even  by  the 
same  artist  are  entirely  different  in  their  handling.  Study 
of  the  technique  of  others  will  soon  convince  the  stiulent 
that  there  is  more  than  one  way  to  paint. 

The  artist  should  understand  all  the  details  of  his  work 


TRAINING    OF  THE  ART  STUDENT.  5 

as  fully  as  the  workman  in  any  of  the  industrial  arts  un- 
derstands the  use  of  his  tools,  but  to  produce  the  best 
work  he  must  express  his  own  personality. 

Undoubtedly  the  first  requisite  for  the  student  is  to  be 
able  to  represent  Nature  truly,  and  this  is  a  point  beyond 
which  very  few  can  expect  to  pass  ;  for  the  poetic  tem- 
perament is  rare,  and  without  it  the  artist  can  simply 
study  Nature.  If  possessed  of  this  temperament,  he  must 
still  "be  able  to  represent  Nature  as  she  appears,  in  order 
to  exercise  his  higher  faculties  in  the  painting  of  com- 
positions and  imaginative  subjects.  The  ability  to  repre- 
sent Nature  truthfully  is  the  first  step  for  the  student,  and 
he  should  be  satisfied  to  study  her  seriously  until  he  has 
attained  a  high  degree  of  perfection.  It  is  so  often  said 
that  the  aim  of  art  should  be  not  reproduction  but  ideali- 
zation, that  the  student  is  likely  to  be  deceived,  and  to 
attempt  to  produce  the  ideal  before  he  can  tnithfully 
represent  Nature.  It  cannot  be  contradicted  that  the 
higher  is  possible  only  through  the  lower,  and  the  student 
must  be  satisfied  to  study  until  he  can  give  easily  and 
truthfully  form,  color,  and  values,  —  in  short,  effects.  To 
produce  a  great  work  of  art  the  mind  must  be  given 
entirely  to  the  result.  This  cannot  be  done  if  the  atten- 
tion is  frequently  diverted  by  drawing,  light,  and  shade, 
and  color.  Through  these  the  painter  should  express 
himself,  as  unconscious  of  means  as  the  orator  through 
words. 


6  FREE-HAND  DRAWING. 

It  is  not  meant  that  the  final  aim  of  the  student  should 

be  the  power  of  photographically  delineating  Nature,  but 

that  careful  study  of  drawing,  values  and  color  should  be 

considered  necessary  to  the  advanced  and  more  valuable 

work  where  the  artist  is  free  to  express  his  feeling. 

'f{        Reproduction  is  impossible.     We  cannot  "  paint  "  even 

//    the  simplest  object.     We  can  only  paint  what  may  create 

,f    a  more  or  less  truthful  impression  of  it.     Many  of  Nature's 

If    effects  are  far  beyond  the  possibilities  of  the  palette,  and 

If    art  must  be  acknowledged  to  be  not  reproduction.     The 

ff    artist  is  thus  justified  in  using  whatever  means  may  best 

1/  answer  his  purpose  of  creating  an  impression  of  the  ideas 

//  Nature  creates  in  him,  and  in  his  highest  work  it  is  a 

f  I  question  not  only  of  what  he  sees,  but  of  what  he  feels. 

The  common  steps  in  the  work  of  the  art  student  are 

I  St.  Drawing  in  outline  from  Nature  and  sometimes 
from  flat  copy. 

2d.  Light  and  shade  in  charcoal  from  casts,  the  antique 
and  still  life. 

3d.   Study  from  life  in  charcoal. 

4th.   Color  study  from  still  life,  life  and  Nature. 

There  is  no  question  but  that  the  color  sense  is  the  most 
difficult  to  cultivate,  and  is  very  rare  at  the  present  time. 
The  deficiency  in  color  perception  is  probably  due  to 
lack  of  training  in  this  direction.  If  the  education  of  the 
color  sense  were  begun  earlier,  undoubtedly  much  good 


TRAINING    OF  THE  ART  STUDENT.  7 

would  result,  and  it  may  be  tnie,  as  some  have  suggested, 
that  if  the  first  instruction  were  in  the  use  of  color,  far 
greater  progress  would  be  made. 

The  great  difficulty  is  that  before  art  instruction  is 
given,  the  students  have  obtained  a  very  practical  knowl- 
edge of  both  the  actual  form  and  its  absolute  color.  The 
knowledge  of  the  form  prevents  the  acceptance  of  its 
appearance,  and  the  mind  is  trained  to  accept  the  image 
of  the  eye  only  after  long-continued  efforts.  The  form 
is  absolute,  and  if  the  efforts  are  continued,  almost  any 
one  can  learn  to  draw  fairly  well.  The  color  of  the 
object  is  absolute,  and  the  mind  knows  this  color  as  well 
as  the  absolute  form  ;  but  the  color  appears  to  change 
in  a  much  greater  degree  than  the  form.  The  form 
appears  to  change  according  to  certain  fixed  and  simple 
laws,  but  the  color  changes  according  to  no  laws  that  can 
be  given  ;  for  the  same  local  color  may  appear  an  infinite 
number  of  different  colors  according  to  light  and  sur- 
roundings, and  it  is  far  more  difficult  to  prove  that  a  yellow 
appears  blue  or  green  or  some  color  not  yellow  to  a 
student  who  cannot  see  it,  than  it  is  to  prove  that  a  hori- 
zontal line  below  the  eye  appears  to  incline  upward  as  it 
retreats. 

The  tendency  of  the  student  who  knows  theories  of 
anatomy,  or  perspective,  or  color  is  too  frequently  to  work 
by  theory  instead  of  by  observation,  and  it  is  a  question 
if  in  many  cases  he  would  not  be  better  off  without  a  care- 


8  FREE-HAND  DRAWING. 

fully  arranged  theory  for  all  conditions.  Certainly  this  is 
so  unless  he  can  be  made  to  realize  that  theory  should 
come  last  and  careful  study  of  Nature  first. 

Though  color  is  so  difficult  to  realize,  it  is  more  impor- 
tant to  the  artist  than  any  other  quality.  We  see  color  first. 
We  may  not  realize  the  appearance  of  the  color,  but  we 
recognize  the  mass  by  the  color,  which  is  flimiliar  to  us 
through  previous  observation.  Form  may  be  almost 
obliteratetl  by  distance  or  other  conditions,  but  the  color 
is  seen,  and  through  it  we  know  the  object.  The  masses 
of  light  and  shade  are  second  in  importance  ;  if  these  are 
correct,  the  effect  of  Nature  is  given  even  if  the  drawing 
of  detail  is  faulty.  This  reverses  the  order  in  which  these 
factors  are  often  arranged,  and  according  to  which  draw- 
ings are  criticised. 

Most  instruction  in  drawing  has  for  its  end  form.  It 
may  be  that  it  is  of  no  use  to  look  for  color,  as  some 
claim,  that  the  student  himself  will  acquire  the  color 
sense ;  but  this  certainly  is  not  true  of  values  (the  rela- 
tions of  the  masses  of  light  and  dark)  which  are  more 
necessary  to  the  effect  of  a  picture  than  absolute  form. 
That  students  do  not  appreciate  the  masses,  or  the  effect 
of  Nature,  is  proven  by  the  numbers  of  pictures  which 
are  so  cut  up  by  exaggerated  detail  that  the  effect  can- 
not be  realized  at  a  proper  distance.  This  criticism, 
more  frequently  than  any  other,  may  be  made  of  the  pic- 
tures in  our  exhibitions.    The  fault  is  due  in  part  to  the 


TJiAIXLYG    OF  THE  ART  STUDENT.  9 

search  for  form  to  the  exclusion  of  other  qualities,  and  it 
seems  t-hat  the  latter  which  are  of  so  great  importance 
should  receive  more  attention,  even  if  the  elaboration  of 
outline  and  detail  at  present  attained,  is  not  secured. 

The  training  of  the  art  student  should  be  more  liberal. 
Instead  of  continually  working  in  one  medium,  as  char- 
coal or  crayon,  and  \iY>on  drawings  of  the  same  size,  he 
should  change  the  medium  or  its  treatment,  and  the  size 
of  the  drawing ;  and  instead  of  always  working  for  form, 
it  is  most  important  that  he  look  for  effect  at  least  part  of 
the  time. 

Drawing  an  object  or  a  figure  by  itself  without  refer- 
ence to  its  surroundings  is  very  good  practice  in  drawing, 
but  this  practice  alone  carmot  prepare  the  student  to 
paint  a  picture,  in  which  there  must  be  atmosphere,  more 
or  less  of  distance,  and  in  which  the  proper  relations  of 
the  parts  to  each  other  must  be  kept.  Moreover,  this 
work  does  not  tend  to  give  the  student  an  idea  of  the 
simplicity  of  the  masses.  It  is  practice  largely  in  draw- 
ing. If  instead  of  representing  the  figure  by  dark  upon 
a  white  surface,  the  effect  of  the  figure  against  the  back- 
ground is  studied  and  the  background  is  represented  of 
its  proper  value,  the  conventional  character  of  the  drawing 
at  once  disappears.  The  result  is  a  picture  instead  of  a 
drawing.  The  student  is  painting  with  charcoal  instead 
of  with  color,  and  is  becoming  familiar  with  the  problems 
he  must  meet  in  his  later  work. 


10  FREE-HAND  DRAWING. 

\V'hen  he  is  not  likely  to  have  a  long  course  of  study,  I 
should  advise  that  drawing  and  values  be  considered  in 
this  way  in  most  if  not  all  of  his  work.  If  the  drawing  is 
from  life,  very  little  time  is  required  to  indicate  the  back- 
ground of  its  proper  value  ;  and  in  drawing  from  still  life 
there  is  no  excuse  for  not  making  a  study  of  effects. 
This  way  is  of  much  more  value  than  that  which  permits 
the  student  in  beginning  to  think  of  only  one  thing  at  a 
time.  When  he  has  formed  this  habit,  it  is  almost  impos- 
sible to  break  away  so  as  to  consider  the  parts  with  refer- 
ence to  the  whole,  and  he  can  certainly  never  look  at 
Nature  as  he  should  until  he  is  able  to  see  the  masses 
and  effects.  The  masses  are  of  the  greatest  importance, 
and  when  our  students  start  by  observing  them,  one  of 
the  chief  difficulties  now  in  their  way  when  they  leave  the 
schools  will  be  removed. 

The  advanced  student  may  sometimes  study  with  ad- 
vantage form  or  local  values  without  a  background.  If 
his  first  study  has  enabled  him  to  see  relative  values,  he 
may  not  need  farther  study  in  this  direction  as  much  as 
special  study,  for  instance  of  the  figure.  In  the  public 
schools,  evening  drawing  schools,  industrial  schools,  and 
all  elementary  and  preparatory  schools,  values  shoul.l  be 
considered  as  important  as  form,  and  all  work  should 
represent  the  object  and  its  background. 

Another  fact  which  docs  much  to  continue  bad  meth- 
ods of  work  is  that  many  art  students,  even  in  advanced 


TRAINING    OF   THE   ART  STUDENT.  11 

schools,  are  either  advised  or  permitted  to  work  from  the 
part  to  the  whole.  Thus  in  a  figure  we  find  them  paint- 
ing the  first  day  the  head,  the  second,  the  shoulders,  and 
so  on,  getting  on  the  last  day  to  the  feet  or  possibly  not 
as  far  as  this,  the  canvas  being  covered  part  by  part.  By 
such  work  it  is  not  possible  to  obtain  a  harmonious  whole. 
In  the  first  place,  it  is  impossible  to  determine  the  effect 
until  the  entire  canvas  is  covered  ;  second,  the  light  and 
color  are  constantly  changing,  the  effect  being  warm  the 
first  day,  cool  the  second,  and  so  on.  Such  a  way  of 
working  does  not  consider  the  effect,  and  it  is  a  wonder 
that  students  trained  thus  produce  as  good  work  as  they 
do. 

The  endeavor  of  the  artist  should  be  to  produce  a 
pleasing  effect  of  color,  light  and  shade,  and  true  values. 
in  short,  a  satisfactory  result.  Why  should  not  the  train- 
ing of  the  student  look  to  these  points?  If  it  is  to  do 
this,  the  student  must  try  to  express  the  effect  as  quickly 
as  possible,  so  that  he  may  be  able  to  change  and  bring 
all  the  detail  into  its  proper  relations.  All  parts  of  the 
drawing  should  be  begun  at  once,  and  should  be  carried 
along  together.  It  is  of  little  importance  how  the  student 
works,  so  long  as  he  has  as  his  aim  the  quickest  possible 
suggestion  of  the  whole  effect.  He  may  draw  with  char- 
coal or  with  the  brush,  or  he  may  make  no  preliminary 
drawing,  as  some  recommend,  but  he  must  get  the  can- 
vas covered  and  the  masses  placed  in  a  short   space  of 


12  FREE-HAND  DRAWING. 

time,  and  in  doing  this  he  is  working  upon  the  most 
important  part  of  the  drawing  all  the  time,  until  the  effect 
is  fairly  obtained. 

First  Study. 

How  shall  the  student  who  is  commencing  the  study 
of  art  best  spend  his  time?  What  shall  he  draw  and 
what  mediums  shall  he  use  ?  As  has  been  stated,  no  one 
method  should  be  permanently  adopted  to  the  exclusion 
of  all  others.  There  is  value  in  all,  and  in  his  later  work 
he  may  find  it  necessary  to  use  many  different  means  of 
expression.  If  we  accept  as  well  founded  the  practice  of 
the  schools,  we  shall  postpone  color,  and  begin  with  the 
pencil  or  charcoal,  making  outline  or  shaded  drawings 
from  casts  or  from  geometric  objects.  In  some  cases, 
students  begin  by  copying  from  the  flat.  Some  benefit 
may  be  derived  from  this  work,  but  it  cannot  be  recom- 
mended. 

The  simplest  drawing  made  from  Nature  is  of  more 
value  than  the  most  elaborate  copy. 

Copying  of  outlines  cannot  assist  one  to  see  the  pro- 
portions for  original  drawings.  Copying  in  other  medi- 
ums can  only  assist  in  the  matter  of  technique,  and  this 
should  not  concern  the  student  at  first.  His  i)roblem  is 
drawing,  and  the  medium  which  allows  him  to  think  of 
the   drawing,  and    does    not    require  thought  about   its 


TRAINING    OF   THE  ART  STUDENT.  13 

handling,  is  tlie  best  for  him  to  use  until  he  can  draw 
fairly  well.     The  pencil  or  charcoal  in  outline  work,  and 
charcoal  in  light_and  shade,  are  means  which  enable  him_ 
to  give  his  entire  thought  to  the  drawing,  and  they  should^ 
be  used  until  form  has  been  mastered. 

He  may  work  from  the  cast  or  from  geometric  objects. 
The  geometric  solids  can  be  obtained  in  complete  sets, 
exactly  made  and  embodying  all  the  type  forms.^  My 
experience  has  led  me  to  believe  that  study  from  these 
objects  for  a  few  weeks  will  give  greater  ability  in  draw- 
ing than  a  similar  amount  of  time  spent  in  any  other  way. 
The  lines  of  a  cast  or  a  figure  are  very  fine,  and  it  is 
more  difficult  to  see  them  correctly  than  those  of  the  geo- 
metric forms,  in  which  foreshortening  and  convergence 
are  illustrated  in  the  simplest  way.  An  untrained  eye 
can  see  the  errors  of  drawing  much  more  easily  in  a  cube 
or  plinth  than  in  the  more  difficult  cast.  Moreover,  the 
means  for  testing  the  appearance  of  the  geometric  forms 
are  so  simple  that  a  child  can  apply  them,  and  discover 
the  errors  of  his  drawing ;  and  when  several  objects  are 
arranged  together,  every  point  is  seen  in  relation  to  so 
many  other  points  that  this  relation  cannot  be  neglected. 
Thus  the  drawing  involves  so  many  problems  that  the 
training  it  gives  is  most  valuable. 

This  work  will  also  give  a  practical  knowledge  of  per- 

1  They  may  be  obtained  of  art  dealers,  also  a  set  of  vase  forms, 
copied  from  the  ancient  Greek. 


i/aZccC' 


14  FREE-HAND  DRAWING. 

spective,  which  will  be  of  great  value  to  the  student  in 
all  his  later  work.  These  subjects  seem  best  for  many 
reasons,  but  the  strongest  one  is  that  the  use  of  the 
thread  to  cover  the  various  edges  and  continue  them  to 
intersect  the  opposite  edges  of  the  group  (see  page  74), 
provides  a  test  so  simple  that  all  can  apply  it,  and  so 
sure  that  it  discovers  at  once  all  serious  errors  in  the 
drawing.  It  makes  the  student  his  own  teacher,  and  if 
he  carries  on  the  drawing  properly,  uses  first  his  eyes, 
then  tests  and  changes  without  erasing  but  by  drawing 
new  Hnes,  he  will  quickly  attain  ability  which  will  enable 
him  to  draw  with  freedom  from  any  subject. 

Frequently  the  student  is  first  required  to  draw  in 
outline.  Sometimes  this  may  be  necessary ;  but  as  cor- 
rect values  are  second  in  importance  to  color,  and  out- 
lines are  of  least  importance,  it  seems  that  when  possible 
he  should  combine  the  study  of  form  and  values  in  a 
light  and  shade  drawing.  If  at  first  the  attention  is  to 
be  given  to  one  medium  for  any  length  of  time,  charcoal 
in  light  and  shade  is  preferable  to  outline  work,  but  the 
best  way  is  an  alternation  of  light  and  shade  with  outline, 
as  explained  on  page  22. 

Lu^ht  and  Shade. 
In  ojder  for  the  drawing  to  be  a  complete  study  of 
values,  the  subject  must  be  represented  with  its  back- 
ground.     It  is  not  meant    that  when  a  group  is  seen 


TRAINING    OF  THE  ART  STUDENT.  15 

against  other  objects,  all  of  these  must  be  carefully 
drawn,  but  that  the  general  value  of  the  background  as 
compared  with  the  group  should  be  given.  It  is  well  at 
first  to  place  the  objects  so  that  they  are  seen  against 
simple  backgrounds,  as  a  sheet  of  gray  paper  or  any 
flat  colored  material.  The  group  should  have  a  strong 
light  coming  preferably  from  the  left  and  from  above. 
When  drawing  from  the  models,  which  are  white,  some 
dark  object  should  always  be  placed  in  the  group.  If 
this  is  not  done,  the  student  will  make  the  shades  too 
strong,  for  by  contrast  with  the  lights  the  shades  seem 
very  dark  when  the  objects  are  strongly  lighted. 
The  drawing  may  be  made  as  follows  :  — 
The  size  and  position  of  the  drawing  should  first  be 
determined  by  suggesting  with  light  and  rapid  strokes  the 
general  effect  of  the  mass  of  the  group.  This  amounts 
to  drawing  the  rough  outline  of  the  group  seen  as  one  / 

object,  as  shown  by  Figs.  5  and  8.  This  drawing,  as  all^  /^  /^  » 
should  be  made  by  the  eye  unaided  by  tests  or  measure-  ' 
ments.  (page  35).  When  made,  it  may  be  tested  by 
measuring  the  apparent  width  and  height  of  the  group 
with  the  pencil,  as  explained  on  page  68.  Within  these 
lines  the  inner  lines  and  the  masses  of  light  and  dark 
should  next  be  suggested,  the  drawing  and  the  light  and,^ 
shade  progressing  at  the  same  time.  The  tendency  is 
to  draw  the  outlines  and  then  put  in  the  shade,  but  it  is 
better  to  allow  the  light  and  shade  to  help  in  the  draw- 


16  FREE-HAND  DRAWING. 

ing,  for  the  masses  of  light  and  dark  are  more  easily  seen 
than  the  edges,  which  are  often  ahiiost  invisible  in  the 
light  or  lost  in  the  shade.  Then  the  cast  shadows  are 
very  important,  and  of  these  the  outline  drawing  takes 
no  account.  There  is  no  preconceived  idea  concerning 
the  shapes  of  the  cast  shadows,  and  thus  the  mind  is  in 
a  condition  to  accept  without  prejudice  the  image  of  the 
eye,  and  the  student  will  find  that  the  shade  and  shadow 
together  form  masses  of  dark,  which  are  more  easily  seen 
and  placed  than  any  other  features.  These  masses  being 
indicated  of  one  value,  it  is  easy  to  strengthen  the  darker 
part  and  thus  bring  out  the  separation  or  Qi\%'^,  whose 
direction  is  often  placed  much  more  truly  by  referring  it 
to  the  shadow,  than  it  would  be  by  drawing  first  the  out- 
lines and  then  the  shadows. 

The  masses  of  dark  should  be  lightly  indicated  at  first, 
in  order  that  they  may  be  moved  about  until  they  are 
rightly  placed.  Whatever  lines  may  be  drawn  as  repre- 
sentations of  edges  should  be  very  liglitly  sketched,  for 

the  same  reason.     It  is  much  better  to  change  bv  draw- 

"       I  II 

ing  a  new  line  slightly  stronger  than  the  first,  and  to  thus^ 
continue  until  the  correct  position  is  secured,  than  to^ 
draw  a  line  and  erase  as  soon  as  it  is  found  incorrect. 


Although    the  student  may  not  see  the   importance  of 
working  in  this  way,  too  much  stress  cannot  be  placed 
on  the  value  of  the  training  obtained  by  bringing   the_ 
drawing  into  place  without  erasing. 


TRAINING    OF  THE  ART  STUDENT.  17 

Figure  i  gives  the  appearance  of  the  sketch  when  the  A-  J__ 
drawing  is  found  to  be  correct.  The  charcoal  may  now 
be  removed  from  the  hghts  by  chamois  skin,  cloth, 
bread,  or  any  kind  of  eraser,  and  the  background  may 
be  carried  as  far  as  is  necessary  This  gives  the  second 
stage  of  the  drawing,  Fig.  2.  For  some  time  it  will  be 
well  not  to  attempt  more  than  the  jalue_s_  of  the  back- 
ground, the  light  (represented  by  a  light  tint  of  char- 
coal), the  shade,  and  the  cast  shadow,  as  in  Fig.  2. 

The  shades  and  cast  shadows  together^  form  dark 
masses  which  are  opposed  to  the  masses  of  light  made 
by  the  surfaces  which  receive  the  direct  rays  of  light ; 
and  the  drawing,  Fig.  2,  must  not  be  regarded  as  simply 
a  stage,  but  as  expressing  a  most  important  fact  which  is 
to  be  kept  in  mind  in  all  the  later  work. 

Many  students  have  great  difficulty  in  seeing  the 
variety  of  light  and  shade  in  Nature,  and  nearly  all  make 
very  serious  errors.  A  common  trouble  is  the  failure  to 
realize  the  difference  between  the  shades  and  shadows 
on  different  colored  objects.  Thus  the  shade  side  of  a 
white  cube  is  made  as  dark  as  that  of  a  red  or  blue  box, 
and  unimportant  detail  in  the  mass  of  either  the  light  or 
the  shade  is  made  so  strong  as  to  entirely  destroy  all  the 
effect,  the  grays  in  the  light  being  as  strong  as  the  shade, 
and  the  reflected  lights  as  strong  as  the  high  lights. 
Such  errors  will  be  made  by  all  until  the  ability  to  look 
at  the  whole  and  not  at  a  part  is  secured. 


/^^^ 


18  FREE-HAND  DRAWING. 

The  effect  can  be  realized  only  when  the  entire  group 
is  seen  at  a  glance,  and  to  do  this  the  vision  must  be 
blurred  until  all  parts  are  seen  equally  and  necessarily 
indistinctly.  This  effect  may  be  obtained  with  the  eyes 
in  focus  for  a  shorter  or  longer  distance  than  that  of 
the  group,  and  is  the  same  as  that  given  by  looking 
through  a  lens  of  tAvelve  or  fifteen  inches  focus.  Open- 
ing the  eyes  is  better  than  nearly  closing  them,  for  this 
cuts  off  most  of  the  light  and  loses  the  color.  In  light 
and  shade  this  is  a  matter  of  not  much  consequence,  but 
it  is  better  to  study  in  light  and  shade  so  as  not  to  be 
obliged  to  change  for  advanced  work. 

The  struggle  comes  in  seeing  for  the  first  time.  A 
lens  of  twelve  inches  focus  has  been  of  great  assistance 
to  many.  By  its  aid  they  have  been  enabled  to  see  the 
masses  and  to  realize  their  errors  when  no  amount  of 
explanation  or  assertion  on  the  part  of  the  teacher  has 
been  of  the  least  value.  Some  recommend  the  reducing 
glass  or  a  Claude  Ix)rraine  mirror,  but  the  blur  glass  is 
the  only  means  that  I  have  been  able  to  use  with  any 
degree  of  success.  After  the  student  has  once  appre- 
ciated the  masses,  and  has  seen  how  unimportant  is  the 
detail  in  these  masses,  he  will  need  no  artificial  help.  A 
little  practice  will  enable  him  to  see  the  entire  group 
without  special  effort ;  in  fact,  to  see  naturally  the  group 
as  a  whole,  and  it  must  not  be  forgotten  that  this  is  the 
only  way  to  see  effects. 


TRAINING    O^  THE  ART  STUDENT.  19 

When  a  number  of  drawings  which  give  simply  the 
masses  of  hght  and  dark,  as  Fig.  2,  have  been  made,  the  /^  -  / 
student  should  try  to  get  all  the  values,  being  careful  that 
the  grays  and  detail  in  the  lights,  and  the  reflected  lights 
in  the  shade,  are  not  made  too  prominent.  He  should 
understand  that  the  first  drawings  made  express  the  most 
important  truth,  that  with  strong  light  there  is  always  the 
contrast  of  well  defined  masses  of  light  and  dark.  The 
tendency  is  to  look  upon  the  drawing.  Fig.  2,  as  simply  a 
stage,  and  to  study  the  detail,  which  can  always  be  found 
upon  close  examination,  so  carefully  as  to  lose  all  general 
effect.  There  is  always  a  tendency  to  exaggerate  the 
slight  differences,  which  appear  greater  than  they  really 
are,  and  the  student  must  struggle  to  keep  the  drawing 
simple.  Frequent  comparison  from  a  distance,  of  the 
draii'ing  with  the  group  is  necessary,  the  drawing  being 
placed  beside  the  group.  If  the  two  are  thus  compared, 
the  effect  being  realized  by  use  of  the  blur  glass  if  the 
student  has  not  yet  learned  to  use  his  eyes,  it  is  thought 
that  if  he  works  earnestly,  he  will  in  a  short  time  be  able 
to  produce  fairly  truthful  representations  of  the  effect. 

Figure  3  represents  the  group  already  studied  with  all  f*^T/ 
the  gradations.  It  will  be  noticed  that  there  is  always 
some  point  in  the  group  that  is  lighter  than  any  other,  as 
the  high  light  on  a  white  vase  or  sphere.  These  points 
should  be  carefully  considered,  and  it  is  evident  that  the 
rest  of  the  masses  of  light  must  be  slightly  gray.     There 


20  FREE-HAND   DRAWING. 

is  also  in  every  group  some  spot  that  appears  darker 
than  any  other.  All  the  other  darks  must  be  compared 
with  this,  and  to  be  sure  of  truth  with  each  other,  as 
must  also  the  grays  in  the  light. 

The  tendency  is  to  make  the  drawing  too  black.  This 
may  be  avoided  by  comparing  the  darks  in  the  group 
with  a  large  piece  of  charcoal  held  in  front  of  them,  and 
shaded  by  the  hand  so  as  to  appear  black.  This  makes 
the  darks  of  the  group  seem  quite  gray. 

There  is  another  point  of  great  difficulty,  and  this  is  in 
regard  to  the  colored  objects ;  for,  as  already  explained, 
colors  do  not  appear  their  real  colors..  The  student  who 
sees  a  colored  object  in  front  of  a  cast  which  is  grayish 
white  immediately  thinks  of  the  actual  color  of  the 
object  in  comparison  with  the  actual  color  of  the  cast. 
The  color  may  be  darker  than  the  cast.  This  being  so, 
it  is  frequently  nearly  impossible  for  him  to  realize  that 
the  color,  even  if  quite  dark,  may  be  so  lightened  by 
direct  light,  as  to  appear  even  lighter  than  the  gray  of 
the  cast  without  a  shadow  upon  it. 

The  statement  is  often  made  that  the  surface  receiving 
the  most  direct  rays  of  light  appears  lightest.  This  is 
not  true  even  for  objects  of  the  same  color.  The  high- 
est lights  are  the  surfaces  that  reflect  the  liglit  most 
directly  to  the  eyes,  not  those  that  receive  the  most 
direct  rays  of  light. 

The   difficulty  increases  if  the  colored  objects   have 


TJiAIXING    OF  THE  ART  STUDENT.  21 

smooth  or  polished  surfaces,  and  frequently  very  dark 
colors  may  appear  much  hghter  than  the  light  objects 
of  the  group,  through  their  reflecting  more  light  to  the 
eye  than  the  lighter  objects.  The  only  safe  rule  for  the 
student  is  not  to  work  by  theory,  or  to  think  how  he 
ought  to  see  the  colors,  but  to  look  for  the  actual  impres- 
sion, remembering  that  this  is  very  likely  to  contradict 
what  he  thinks.  After  having  frequently  made  his 
drawing  exactly  opposite  from  what  it  should  be,  the 
student  should  have  no  difficulty  in  transferring  his 
dependence  upon  his  ideas  to  his  eyes.  When  this 
step  has  been  taken,  Nature  is  before  him  as  an  open 
book,  to  be  studied  when  he  wishes,  and  it  is  no  longer  a 
question  of  seeing,  but  of  the  best  way  to  do  what  he  feels. 
A  point  which  must  be  carefully  guarded  against  in  all 
work  is  the  hardness  that  comes  from  definite  lines,  and 
sharp  separations  between  the  different  parts.  The  eye 
sees  but  a  point  at  any  one  time.  This  point  is  seen 
clearly,  all  oUier  points  indistinctly,  so  that  tlie  effect  of 
Nature  cannot  be  given  by  a  drawing  in  which  all  the 
edges  and  separations  are  brought  out  by  hard  lines.  In 
Nature  there  are  no  lines.  We  see  objects  through  con- 
trasts of  color  and  light  and  shade,  and  we  do  not  see 
sharp  definitions  between  the  different  colors.  Even  the 
straight  edges  of  the  models  are  not  seen  as  sharp  lines, 
the  atmosphere  and  the  action  of  the  eye  causing  them 
to  blur  and  soften. 


22  FREE-HAND  DRAWING. 

The  drawing  must  be  definite  without  being  haul. 
Frequently  the  outlines^are_entij:gly^lost^.  This  occurs  in 
the  shadows  or  in  the  mass  of  the  light,  and  particularly 
is  it  true  of  detail  in  casts.  Generally  the  outlines  dis- 
appear for  a  short  distance  only.  The  student,  knowing 
the  form,  is  very  apj  to  supply  the  missingjiart,  and  draw 
what  he  does  not  see,  and  thus  his  drawing  becomes  hard 
and  cut  up.  If  he  will  study  the  effect  and  draw  only 
what  he  sees,  avoiding  sharp  edges  and  hard  separations, 
he  cannot  fail  to  make  a  good  drawing. 

I  have  described  the  way  in  which  the  student  should 
work  to  produce  the  finished  light  and  shade  drawing, 
but  do  not  advise  him  to  spend  all  his  time  in  this 
work,  for  I  think  great  benefit  will  result  from  the  study 
of  outline  simply.  It  is  better  from  the  start  for  him  to 
give  part  of  this  time  to  pencil  outline.  I  say  pencil  in 
preference  to  charcoal,  because  erasures  should  not  be 
made  until  the  correct  outline  is  secured.  If  charcoal 
is  used,  it  is  impossible  to  make  many  changes  with- 
out erasing.  With  a  medium  pencil  the  lines  may  be 
given  many  different  positions,  the  last  line  being  slightly 
strengthened  each  time,  and  the  correct  result  obtained 
without  erasing  a  line.  The  training  thus  given  is  very 
valuable.  I  would  have  drawings  made  in  this  way  from 
the  models,  until  groups  of  five  or  six  of  the  most  diffi- 
cult ones  can  be  correctly  drawn  in  an  hour  or  two.  In 
finishing  the  drawings,  the  lines  should  be  accented  as 
explained  on  page  44. 


TRAINING    OF   THE  ART  STUDENT.  11 

In  connection  with  this  work  the  student  will  find  that 
the  making  of  quick  sketches  in  a  note-book,  with  a  soft 
pencil,  will  greatly  assist  to  freedom  and  accuracy.  These 
sketches  may  be  made  complete  studies  of  light  and 
shade  and  values ;  and  if  one  is  made  each  day,  beginning 
with  simple  objects,  he  will  soon  be  able  to  draw  freely 
and  well  a  group  of  several  objects. 

I  have  said  little  about  tests.  He  who  intends  to 
study  art  as  a  profession,  or  even  as  an  accomplishment, 
should  be  able  to  depend  upon  his  eyes,  and  should  use 
few  tests.  The  following  tests  are  sufficient :  The  pencil 
for  measuring  proportions,  and  held  in  front  of  lines  '  ff 
to  give  their  angles,  or  held  horizontal  or  vertical  for 
comparisons,  and  in  beginning,  the  use  of  the  thread,  and 
later,  the  passing  of  the  pencil  point  over  the  lines  or  the 
drawing  in  the  air.  If  he  cannot  succeed  with  these,  his 
time  will  be  better  spent  in  other  work.  Under  the  head- 
ing of  tests,  in  the  latter  part  of  this  book,  are  given  several 
means  for  assisting  the  pupil  to  apply  the  tests  correctly, 
but  these  •  are  intended  for  public  school  teachers  who 
have  to  teach  those  without  special  ability,  and  though 
such  aids  may  be  necessary  in  these  cases,  they  should 
not  be  required  by  the  art  student. 

Use  of  Materials. 

At  first,  the  matter  of  technique  and  handling  is  of  no 
importance  to  the  student,  whose  only  aim  should  be  to 


^a^Cc^uc^ 


24  FREE-HAND  DRAWING. 

obtain  good  drawing  and  correct  values.  By  this  we  do 
not  mean  that  it  is  of  no  importance  how  the  student 
works,  for  he  may  work  in  bad  ways  and  with  unworthy 
ends  in  view.  We  mean  that,  having  as  a  result  the  pro- 
duction of  drawings  true  in  effect,  in  as  direct  a  manner 
as  possible,  he  is  not  likely  to  waste  time  over  a  way  of 
handling  which  does  not  tend  to  this  result,  for  the  earnest 
and  honest  student  is  thinking  of  the  effect  rather  than 
the  execution  of  the  drawing.  It  is  interesting  to  see 
clever  handling  and  brilliant  execution,  and  they  are  to 
be  desired,  but  the  student  should  not  try  for  them. 
Cleverness  and  style  will  come  of  themselves  in  time.  If 
the  student  tries  for  these,  he  may  .secure  them,  but  prob- 
ably at  the  expense  of  the  substantial  qualities  which 
make  a  strong  picture.  He  should  be  satisfied  to  study 
Nature  and  work  earnestly  until  a  true  representation  of 
her  is  obtained.  This  drawing  is  much  more  valuable, 
even  though  the  labor  spent  upon  it  is  evident,  than  the 
most  clever  study  which  is  untrue.  Honest  study  gives 
the  knowledge  which  in  time  enables  one  to  express 
directly,  and  thus  with  an  interesting  handling. 

Not  only  does  this  honest  study  of  Nature  and  appear- 
ances produce  the  most  valuable  results,  but  from  the 
start  it  is  most  interesting  to  the  student  who,  each  time 
that  he  discovers  a  new  fact,  experiences  the  pleasure  of 
an  investigator  in  a  new  field,  and  with  each  new  idea, 
he  presses  on  with  renewed. vigor. 


TRAINING    OF  THE  ART  STUDENT. 


25 


That  this  study  is  interesting  to  all,  even  the  youngest, 
is  shown  by  Viollet  Le  Due,  in  his  most  valuable  work, 
"  Learning  to  Draw."  His  illustration  of  little  Jean's 
drawing  of  the  cat  strikes  the  keynote  of  the  present 
tendency  in  art ;  and  Jean's  replies  to  his  questions  may 
be  studied  with  great  profit  by 
many  teachers.  Especially  when 
in  answer  to  the  question,  "  Do 
they  teach  you  to  draw  at  school? " 
he  replies,  "  No,  sir  ;  they  teach  us 
to  make  only  rounds  and  squares." 

A  stick  of  soft  charcoal  should 
be  used  for  all  except  the  careful 
drawing  of  the  finishing  touches. 
In  the  first  stage  the  side  of  the 
charcoal  may  be  placed  upon  the 
paper,  and  even  tints  be  produced 
by  a  regular  motion  and  uniform 
pressure,  each  movement  making 
a  wide  tint,  and  only  a  few  seconds  being  required  to 
cover  the  background  or  any  other  large  surface.  In  the 
later  work  for  the  careful  drawing,  it  will  be  necessary  to 
use  a  stick  of  hard  charcoal  sharpened  to  a  chisel-shaped 
point. 

Some  teachers  insist  that  the  drawing  shall  be  made 
entirely  by  the  use  of  the  point  of  the  charcoal,  and 
allow  no  softening  or  blending  even  by  the  finger,  and 


LITTLE  JEANS    DRAWING. 


26  FREE-HAND  DRAWING. 

even  beginners  in  the  public  schools  are  obliged  to  render 
light  and  shade  by  a  hatching  of  lines  as  in  a  lithograph. 
Adherence  to  any  such  rules  will  cause  much  loss  of  time  ; 
for  sometimes  one  way  is  quickest,  and  sometimes  another. 
But  to  make  a  light  and  shade  drawing  by  means  of  lines 
is  the  most  difficult  and  slowest  way  imaginable,  and  the 
student  is  advised  to  defer  all  ways  of  handling  which  are 
difficult  and  slow,  to  the  time  when  he  may  pursue  these 
methods  for  training  simply  in  their  handling,  and  not  as 
mediums  for  the  study  of  light  and  shade.  He  should 
work  for  effects  until  he  can  render  them  truly,  and 
should  not  allow  himself  to  be  trammelled  by  arbitrary 
rules  or  difficult  ways  of  working.  He  should  aim  to  get 
good  drawing  and  values  in  the  shortest  time,  and  all 
means  which  accomplish  this  should  be  legitimate. 

Some  teachers  advise  the  use  of  the  stump,  the  char- 
coal being  rubbed  by  it  to  an  even  tint.  The  objection 
to  "  stumping "  is  that  the  pupils  seem  to  think  that 
smoothness  is  a  virtue,  and  all  that  is  necessary  is  to  move 
the  stump  about  vigorously,  and  in  some  way  or  other  the 
stump  will  make  the  drawing.  Such  use  of  the  stump  not 
only  quickly  spoils  the  paper,  but  tends  to  create  the 
idea  that  the  drawing  cannot  be  made  directly.  The 
stump  may  be  used  with  advantage,  to  place  the  charcoal 
in  parts  too  small  for  the  finger,  and  for  lifting  the  lights, 
but  the  tendency  to  use  improperly  is  so  strong  that  no 
rubbing  with  the  stump  should  be  allowed. 


TRAINING    OF   THE  ART  STUDENT.  27 

In  order  to  get  atmosphere,  it  will  frequently  be  neces- 
sary to  fill  in  the  grain  of  the  paper  by  moving  the  char- 
coal about  until  the  depressions  of  the  paper  have  received 
a  tint.  This  may  be  done  by  very  lightly  passing  the 
finger  over  the  paper.  When  the  grain  of  the  paper  has 
been  filled  in  this  way,  the  drawing  should  be  finished,  as 
directly  as  possible,  with  the  point  of  the  charcoal,  a  tint 
of  the  proper  strength  being  placed  by  careful  drawing 
just  where  it  is  wanted.  If  a  small  part  has  been  made 
too  dark,  it  may  be  lightened  by  touching  with  the  finger 
or  stump  ;  a  large  part,  by  blowing  off  the  charcoal.  The 
lights  may  be  drawn  with  an  eraser.  Faber's  eraser 
made  in  pencil  form  is  good  for  this  work,  and  the  fine 
lines  of  light  may  be  taken  out  with  the  hard  eraser 
called  "  Nigrivorine,"  which  should  be  cut  to  a  thin  edge 
wide  enough  to  be  strong.  Bread  rolled  into  the  form  of 
a  pencil  is  the  best  eraser.  It  will  quickly  remove  almost 
all  the  charcoal  from  a  large  surface  without  injury  to  the 
texture  of  the  paper. 

When  the  drawing  is  finished,  it  must  be  sprayed  with 
fixatif.  This  should  be  applied  with  great  care.  If 
drops  are  allowed  to  form  on  the  paper,  they  will  float  the 
charcoal  and  spoil  the  drawing.  If  too  much  is  applied, 
the  drawing  will  shine  and  lose  its  life.  It  should  be 
applied  a  little  at  a  time  and  allowed  to  dry  between  the 
applications.  It  is  well  to  avoid  too  much  surface  char- 
coal, on  account  of  the  difficulty  of  fixing  the  drawing 


28  FREE-HAA'D  DRAWING. 

without  floating  it  over  the  paper  and  thus  spoiling  the 
drawing. 

The  darkest  parts  will  require  more  fixatif  than  the 
light  parts.  It  can  be  placed  upon  these  parts  by  cover- 
ing the  drawing  with  a  paper  in  which  a  hole  is  made  of 
the  size  of  the  place  needing  fixatif.* 

Having  described  the  ways  in  which  the  student  may 
study  to  obtain  facility  in  drawing,  I  wish  to  say  that  he 
who  can  draw  and  render  values  in  charcoal  is  ready  to 
work  in  any  medium,  and  after  the  first  experiments 
necessary  to  a  new  medium,  he  will  do  so  with  success  if 
he  understands  that  whatever  the  medium,  the  problem  is 
the  same,  and  is  simply  and  always  drawing  and  values 
and  color. 

There  are  too  many  who  paint  by  receipt,  but  there 
should  be  no  such  thing  as  a  nile  or  a  way  of  doing,  as 
many  seem  to  think,  when  they  ask  how  to  represent 
trees,  or  grass,  or  drapery,  etc.  To  all  who  would  be 
serious,  the  problem  is  simply  observation ;  and  since 
Nature  is  always  different,  there  can  be  no  receipts  for 
representing  her  infinite  variety. 

Some  students  seem  to  think  that  they  are  commenc- 
ing a  new  subject  when  taking  up  a  new  medium.     This 

^  Fixatif  may  be  made  by  dissolving  white  shellac  in  pure  alcohol. 
The  alcohol  should  stand,  after  the  gum  has  been  dissolved,  long  enough 
for  the  impurities  to  settle  at  the  bottom.  The  upper  part  will  then  be 
of  a  clear  amber  color.  It  may  be  turned  into  another  bottle,  and  if  too 
strong,  diluted  so  that  a  drop  will  evaporate,  leaving  just  a  trace  of  gum. 


TRAINING    OF  THE  ART  STUDENT.  29 

is  not  so,  for  the  subject  is  always  the  same,  and  the 
treatment  should  be  the  same  in  striving  first  for  the 
masses  and  the  effect. 

The  most  frequent  error  of  all  is  the  attempt  to  finish  a 
part  before  the  effect  is  indicated.  Much  time  is  spent 
in  carefully  drawing  and  finishing  a  part,  only  to  find  when 
the  rest  is  in  place  that  it  is  out  of  drawing  or  incorrect 
in  values.  The  drawing  should  begin  and  progress  all 
at  once  and  equally  until  the  desired  effect  of  the  masses 
is  attained,  when  the  detail  may  be  studied.  The  more 
quickly  the  white  paper  or  the  canvas  is  covered,  the 
better,  and  until  the  values  and  masses  are  nearly  cor- 
rect nothing  else  should  be  considered. 

There  are  so  many  drawings  and  paintings  which  are 
merely  conventional  pretty  things,  that  the  student  may 
have  difficulty  in  realizing  that  they  are  not  true,  and  that 
his  work  should  be  serious  and  honest.  It  is  hoped  that 
soon  a  higher  standard  may  be  placed  before  the  art  stu- 
dent, that  he  may  understand  that  not  all  hjs_problem  is 
in  the  drawing,  but  that  values  and  color  areequallyand 
even  more  important  thanjibsolute  form,  and  that  he 
may  acquire  the  power  to  represent  Nature  easily  and 
tnithfully. 


CHAPTER   II. 
Outline  Drawing. 

It  is  often  said  that  there  are  no  outUnes  in  Nature. 
In  a  way  this  is  true,  out  it  cannot  be  understood  to 
mean  that  form  is  unnecessary  or  that  it  may  be  slighted. 
The  student  cannot  learn  to  paint  or  to  make  pictures 
in  any  medium,  without  drawing  the  forms  of  the  objects. 
The  defining  of  the  lights  and  shades  and  the  various 
bits  of  color  which  are  seen  in  Nature  is  necessary  to 
give  solidity  and  character  to  a  picture,  and  it  is  useless 
to  think  that  anything  can  be  accomplished  with  color  or 
light  and  shade  if  approximate  representations  of  form 
cannot  be  made. 

Every  object  has  definite  form  and  size,  and  though 
it  may  not  be  outlined,  it  has  boundaries.  Although  the 
representation  of  objects  in  outline  only,  is  at  best  a 
conventional  and  imperfect  means  of  expression,  so  far 
often  as  even  form  is  concerned,  the  student  can  be 
taught  to  observe  effects,  and  may  often  succeed  in  con- 
veying a  fair  impression  of  the  character  of  the  object, 
and  of  varieties  of  surface  and  texture.  He  will  find 
that  the  study  of  appearances  and  their  representation, 
30 


OUTLINE  DRAWING.  31 

as  fully  as  possible,  even  in  so  simple  a  way  as  outline 
drawing,  will  in  great  measure  prepare  the  way  for  work 
in  light  and  shade  and  color.  The  whole  question  is 
simply  one  of  seeing,  and  the  student  should  not  trouble 
himself  over  technique,  as  his  only  aim  should  be  a  true 
representation  of  Nature. 

The  most  important  points  in  free-hand  drawing  are 
freedom,  directness,  and  accuracy.  It  is  difficult  to  give 
directions  which  will  produce  these  results,  as  individu- 
ality will  prevent  all  from  working  in  a  uniform  way,  and 
handling  and  technique  are  of  little  importance.  Since 
the  production  of  truthful  drawings  is  the  end  desired,  it 
is  of  no  consequence  that  such  drawings  are  produced 
by  different  persons  in  different  ways,  but  it  may  be  well 
to  give  a  few  general  directions. 

It  is  most  important  that  the  pencil  should  be  held 
lightly,  and  the  first  lines  of  the  drawing  suggested  freely 
and  rapidly.  The  paper  should  be  not  less  than  eleven 
by  fifteen  inches,  and  the  drawings  should  be  large,  as 
small  drawings  will  produce  a  mechanical  way  of  work- 
ing. A  long  pencil  will  assist  to  freedom  of  motion.  It 
may  be  held  as  a  stick  of  charcoal  between  the  thumb 
and  first  two  fingers,  and  as  far  as  possible  from  the 
point. 

The  paper  should  be  fastened  upon  the  board  with 
its  edges  parallel  to  those  of  the  board.  If  the  edge  of 
the  paper  is  not  straight,  a  horizontal  line  may  be  drawn 


32  FRRE-HAND   DRAWING, 

near  its  lower  edge,  so  that  directions  may  be  referred 
to  this  line.  Ikfore  attempting  to  draw  any  object,  the 
student  should  accjuire  the  frei'dom  of  motion  which  is 
necessary  to  good  work,  by  drawing  lines  in  all  direc- 
tions.  Curved  lines  may  be  produced  by  swinging  the 
pencil  from  the  wrist,  clboWj  or  shoulder  Jand  straight, 
lines  l)y  a  motion  of  the  entire  ami.  These  movements 
should  l)e  practised  imtil  lines  can  be  drawn  instantly 
across  the  i)ai)er  in  any  direction.  This  free  motion  is 
most  important  for  all  sketching,  but,  jn  finishing  or 
accenting  a  drawing,  whose  ])roportions  h.ive  been 
thus  sketched,  more  pressure  will  be  recpiired,  and  the 
pencil  may  be  heKl  more  firmly  and  nearer  the  point. 

The  first  subjects  may  be  the  geometric  solids,  or  anv 
common  objects.  I  will  explain  the  way  in  which 
these  may  be  studied,  by  making  a  sketch  of  a  box  with 
its  cover  thrown  back.     (See  I'ig.  4.)      A'/'V ^~ 

First,  nearly  close  the  eyes  and  try  to  sec  the  l^ox,  not 
ns  a  solid,  but  as  a  silhouette,  the  outline  of  the  mass  of 
the  box  against  the  background  being  what  sh«Mil(l  first  be 
carefully  studied.  A  little  practice  with  the  eyes  nearly 
closed  will  enable  one  to  see  the  mass  in  this  way.  ( Mg.  5 .) 

In  order  to  realize  the  directions  whi(-h  tiie  e<lges 
ap|H\nr  to  have,  lines  may  be  <lrawn  in  the  air,  by  mov- 
ing the  pent'il  point  so  that  it  appears  to  cover  the  edges. 
When  this  is  done,  care  shouhl  be  taken  not  to  move  the 
pencil  away  frotn  the  eyes,  that  is,  in  the  a«tu,d  direc- 


OUTLINE  DRAWING.  33 

tion  of  the  edges,  but  to  keep  the  pencil  point  where  it 
would  be  if  it  were  held  upon  a  pane  of  glass  placed 
directly  in  front  of  the  student.  This  test  is  the  most 
valuable  of  all,  because  it  is  the  simplest  and  easiest  to 
apply.  It  is  really  the  same  as  the  use  of  the  thread, 
exi)lained  on  page  74,  and  nearly  all  other  means  of 
testing  will  at  last  be  discarded  in  favor  of  this  first  and 
simplest. 

After  careful  study  of  the  mass,  its  oudine  may  be 
lightly  sketched,  no  measurements  of  proportion  having 
been  made,'  The  aim  is  to  train  the  eye  to  see  cor- 
rectly. In  order  to  do  this,  the  student  must  depend 
upon  his  eye,  and  put  down  its  first  impression,  rather 
than  the  results  of  mechanical  tests  of  proportions.  He 
must  first  draw,  and  then  test  by  measuring. 

When  the  outline  of  the  mass  has  been  sketched^  the 
inner  lines  may  be  drawn,  and  the  result  carefully  studied 
to  see  that  it  agrees  with  the  appearance.  When  it  is  as 
near  as  can  be  seen,  the  drawing  may  be  tested  by  meas- 
uring the  proportions  as  explained  on  page  68.  If  the 
sketch  does  not  agree  with  these  tests,  it  must  be 
changed.  .Ml  changes  should  be  made,  not  by  erasing, 
but  by  drawing  new  lines,  and  the  drawing  should  be 
earned  on  in  this  way,  until  the  correct  lines  are  found. 

The  first  lines  must  be  ver}'  light.  As  changes  are 
made,  the  strength  may  be  increased  to  distinguish  them, 
until  the  correct  line  is  secured.     The  drawing  having 

'  These  lines  are  approximate,  and  little  time  should  be  given  them.  See 
page  15. 


34  FREE-HAND  DRAWING. 

been  changed  to  agree  with  the  measurements  of  the 
whole  height  and  width,  and  tested  by  moving  the  pencil 
point  to  cover  the  edges,  it  will  be  well  to  test,  by  means 
of  vertical  and  horizontal  lines,  taken  through  the  differ- 
ent angles  of  the  box.  Thus,  drop  the  pencil  point  verti- 
cally from  point  i,  and  see  where  it  cuts  the  lower  edge, 
and  carry  the  point  horizontally  from  point  2,  and  note 
its  intersection  with  the  front  edge.  The  pencil  may  now 
be  made  to  continue  the  apparent  directions  of  the 
edges  A,  B,  C,  etc.,  until  the  points  where  the  continued 
lines  appear  to  intersect  the  opposite  outlines  are  noted. 
These  tests  may  also  be  applied  by  the  pencil  used  as  a 
straight  edge  and  held  horizontal  and  vertical,  and  to 
appear  to  coincide  with  lines.  These  tests,  if  carefully 
made,  will  produce  a  drawing  which  is  practically  true, 
and  should  be  depended  upon.  The  first  measurements 
of  height  and  width  should  be  very  carefully  taken. 
Distances  which  are  nearly  equal,  as  EF  and  FG,  may 
also  be  compared,  but  as  a  rule,  few  measurements  of 
proportion  should  be  made,  as  short  distances,  or  short 
with  long  distances,  cannot  be  compared  with  sufficient 
accuracy  to  be  of  any  value.    (Fig.  6.) 

The  thread  may  be  used  instead  of  the  pencil  for  tests, 
as  explained  on  page  74.  The  thread  appears  a  fine 
line,  whose  intersections  with  the  edges  may  be  easily 
placed,  so  that  until  the  eye  can  be  depended  upon  the 
thread  is  preferable  to  the  pencil. 


OUTLINE   DRAWING.  35 

It  is  most  important  that  all  changes  be  made,  not  by 
erasing,  but  by  drawing  new  lines.  Erasing  and  keeping 
but  one  line  from  first  to  last  will  surely  produce  a  hard_ 
and  inaccurate  drawing ;  and  although  it  may  finalj^be  . 
made  to  agree  with  all  the  tests,  it  will  still  be  lacking  in 
spirit.  It  is  difficult  at  first  for  most  students  to  draw 
lightly  enough  to  secure  the  correct  lines  without  too 
great  heaviness,  but  it  is  better,  rather  than  to  erase,  to 
throw  the  drawing  away  and  start  anew  until  the  result 
can  be  secured  without  having  lines  so  black  that  they 
cannot  be  easily  erased. 

The  reason  for  working  in  this  way  is  that  we  wish  the 
student  to  depend,  as  for  as  possible,  on  his  eyes.  If  he 
erases  and  has  one  line  from  the  start,  unnecessary  time  is 
given  to  the  drawing,  and  he  will  hesitate  to  erase  his  lines. 
If  light  lines  are  drawn  and  not  erased,  but  others  drawn 
as  soon  as  there  is  doubt  about  the  first  being  rightly 
placed,  the  student  is  much  more  free  to  change  as  each 
suggestion  occurs,  and  toward  the  last  he  has  his  choice  of 
the  various  lines  already  drawn  and  can  experiment  freely. 

This  is  by  far  the  quickest  and  most  accurate  way,  and 
prepares  for  rapid  and  truthful  sketching.  It  is  difficult 
at  first  for  the  student  who  has  been  taught  the  mechani- 
cal way  of  drawing  one  line  at  a  time,  but  he  will  not 
have  to  draw  very  long  in  this  way  before  he  will  be 
able  to  produce  truthful  sketches  without  drawing  many 
unnecessary  lines. 


36  FREE-HAXD  DRAWING. 

There  is  not  much  choice  of  pencils  for  this  part  of 
the  work,  but  it  is  well  to  use  always  as  soft  a  one  as  the 
nature  of  the  work  will  permit.  As  no  pressure  should 
be  used,  the  lead  making  at  first  as  light  a  line  as  can  be 
seen,  and  as  all  lines  except  the  correct  ones  must  be 
erased,  there  is  no  reason  why  the  student  who  has  diffi- 
culty in  using  a  soft  pencil  should  not  use  a  hard  one 
until  the  drawing  is  ready  to  accent. 

When  the  correct  outline  has  been  found,  it  is  neces- 
sary to  finish  the  drawing.  The  paper  must  first  be 
cleaned,  all  the  lines  except  the  last  being  erased.  The 
easiest  way  to  reserve  these  lines  is  to  make  them 
stronger  than  the  others  so  that  they  will  show  faintly, 
when  the  eraser  has  been  passed  over  the  paper,  remov- 
ing all  but  an  indication  of  the  result 

The  drawing  may  now  be  accented  with  a  soft  pencil. 
The  pencil  may  be  held  more  firmly,  and  the  lines  drawn 
of  their  proper  strength  by  one  touch,  the  attempt  being 
not  to  produce  a  fine  even  line  in  imitation  of  a  ruled 
one,  but  rather  a  line  of  medium  strength  which  will  con- 
vey the  idea  of  straight  edges.  For  the  present  it  is 
better  for  the  lines  to  be  made  of  uniform  strength,  with 
no  attempt  at  gradation,  or  the  frequent  conventional 
accenting  of  the  nearer  edges  by  heavier  lines.  This 
point  will  be  considered  later,  but  we  wish  now  to  advise 
the  student,  if  he  is  already  familiar  with  it,  to  forget  it 
as  quickly  as  possible,  and  to  finish  in  lines  of  one 
strength  or  as  explained  on  page  44. 


OUTLINE  DRAWING.  37 

The  student  should  draw  from  various  objects  in  dif- 
ferent positions,  until  he  is  able  to  see  them  very  nearly 
correctly  at  first.  The  time  required  for  this  will  depend 
wholly  upon  the  pupil  and  the  care  with  which  directions 
are  followed. 

Groups. 

After  the  practice  from  single  objects,  several  should 
be  arranged  in  a  group.  The  student  will  probably 
attempt  to  draw  the  objects  one  at  a  time,  taking  first  the 
prism  A,  Fig.  7,  next  the  vase  B,  then  the  cylinder  C, 
and  last  the  frame  D.  The  objection  to  this  way  of  pro- 
ceeding is  that  as  the  objects  are  drawn  one  at  a  time, 
until  the  last  is  completed,  the  proportion  of  the  whole 
group  —  that  is,  its  greatest  height  in  comparison  with  its 
greatest  width  —  cannot  be  seen.  Indeed,  this  is  often  not 
even  considered,  the  student  taking  it  for  granted  that 
since  he  measured  and  tested  each  object  as  it  was 
drawn,  the  single  objects  are  correct,  and  therefore  the 
group.  But  from  what  has  been  said  it  will  be  seen  that 
each  object  is  likely  to  be  a  little  out  of  proportion  ; 
indeed,  we  may  say  is  sure  to  be  so.  This  being  the  case, 
the  errors  are  multiplied  ;  and  if  the  height  and  width  are 
compared,  the  proportion  is  found  to  be  far  from  correct. 
It  is  a  principle  generally  acknowledged  that  in  all  teach- 
ing the  whole  should  be  presented  before  its  parts,  and  it 
cannot  be  contradicted  that  adding  one  object  to  another 


38  FREE-HAND  DRAWING. 

until  finally  the  patchwork  is  complete  is  an  uneduca- 
tional  way  of  proceeding.  Practically  it  is  also  most 
unsatisfactory,  as  with  each  object  the  difficulties  in- 
crease, and  at  last  it  becomes  impossible  to  place  the 
drawings  where  they  belong.  The  only  logical  way  is  to 
draw  the  group  all  at  once,  first  considering  it  as  a  mass 
and  blocking  in  its  proportions  by  lines  passing  from  the 
principal  points.  Fig.  8.  When  these  lines  have  been 
drawn  and  considered,  they  may  be  tested  by  measuring 
the  whole  height  and  width,  and  the  directions  tested 
by  use  of  the  thread  or  pencil  as  explained. 

A  good  plan  is,  as  soon  as  the  proportions  have  been 
determined,  to  draw  horizontal  and  vertical  lines  forming 
a  rectangle  enclosing  the  drawing,  and  to  be  careful  that 
the  drawing  is  kept  within  these  lines.  The  proportions 
of  the  whole  group  being  thus  determined  as  nearly  as 
measurements  can  determine,  the  objects  may  now  be 
sketched  by  eye,  the  most  important  lines  being  drawn 
first.  These  are  the  lines  whose  positions  and  directions 
are  most  easily  seen.  They  are  the  longest  lines,  lines  of 
one  object  which  are  nearly  continuations  of  those  of 
some  other  object,  and  lines  which  are  brought  out  dis- 
tinctly by  shade  or  shadow.  It  is  evident  that  in  this 
way  the  drawings  of  the  different  objects  are  proceeding 
at  the  same  time,  and  the  shorter  and  less  prominent 
lines  being  drawn  last,  the  group  may  be  said  to  be  drawn 
all  at  once,  or  as  if  a  single  object  having  many  parts. 


OUTLINE  DRAWING.  39 

While  drawing,  the  student  must  think  of  the  tests, 
appUed  by  the  thread,  of  horizontal  and  vertical  lines, 
and  of  continued  lines  ;  and  drawing  in  the  air  by  passing 
the  pencil  point  to  hide  the  edges  to  be  represented,  will 
help  greatly.  The  object  should  be  studied  in  this  way 
and  changed  as  often  as  found  incorrect,  until  the  eye 
can  do  no  more.  It  is  now  time  to  apply  systematically 
the  tests  explained  by  the  drawing  of  the  box. 

The  first  test  is  to  compare  the  height  and  width  of 
each  object  of  the  group,  and  also  to  compare  these 
dimensions  with  those  of  the  whole  group.  This  test  is 
the  most  important,  and  should  be  very  carefully  taken. 
Slight  inaccuracy  can  hardly  be  avoided,  but  these  dimen- 
sions are  the  longest  measurements,  and  can  be  compared 
more  accurately  than  any  others,  especially  in  the  case  of 
those  which  are  nearly  equal,  and  the  best  that  can  be 
done  is  to  make  the  drawing  agree  wkh  these  measure- 
ments. By  this  time  the  student  should  be  able  to  meas- 
ure as  accurately  as  these  drawings  require. 

These  tests  will  generally  change  the  drawing  through- 
out. The  changes  should  be  made,  not  by  erasing,  but 
by  adding  lines,  and  without  other  measurements  until 
the  eye  can  see  no  more  to  be  done.  The  thread  may 
then  be  used,  first  for  the  tests  of  horizontal  and  vertical 
lines,  second  for  the  continuing  of  all  the  edges,  and  third 
for  covering  points  in  the  group  opposite  one  another, 
that   the  intersections  of  these  diagonal  lines  with   the 


40  FREE-HAND  DRAWING. 

edges  may  be  noted.  The  thread  used  thus  will  discover 
every  discrepancy  except  the  slight  deviations  which 
only  the  accurate  eye  can  detect.  After  the  training 
which  is  given  by  these  drawings  made  entirely  by  eye 
before  any  tests  are  applied,  this  accuracy  will  soon  be 
secured. 

When  the  correct  lines  have  been  found,  the  others 
are  to  be  erased,  as  explained  on  page  36,  and  the  draw- 
ing is  to  be  accented.  But  now  the  student  will  do  well 
to  think  of  effect,  and  to  see  if  more  interest  and  expres- 
sion cannot  be  given  to  the  drawing  than  is  given  by  uni- 
form lines.  The  student  has  perhaps  been  taught  that 
the  nearest  objects  are  seen  most  strongly,  and  that  the 
strength  diminishes  with  the  distance.  This  of  course  is 
true  in  a  general  way.  It  is  the  effect  of  aerial  perspec- 
tive, or  the  changing  of  color  by  intervening  atmosphere. 
Thus  of  a  row  of  Hght  objects  the  nearest  will  appear  the 
lightest  and  brightest,  and  of  a  number  of  dark  objects 
the  nearest  will  appear  the  darkest.  The  light  object  in 
the  distance  appears  darker,'  and  the  dark  one  lighter, 
and  in  a  sketch  representing  considerable  distance  this 
principle  will  be  of  assistance.  But  it  must  be  stated  so 
as  not  to  convey  the  idea  that  there  can  be  nothing  in 
the  distance  as  strong  or  stronger  than  the  unimportant 
features  of  the  foreground,  for  we  do  not  see  objects 
more  or  less  distinctly  according  to  their  distance  ;  in  fact, 

1  Very  light  objects  may  change  but  little. 


OUTLINE  DRAWING.  41 

distance  has  practically  nothing  to  do  with  it.  We  distin- 
guish  objects  as  masses  of  color,  lighter  or  darker  than  the 
colors  against  which  they  are  seen.  This  being  so,  it  is 
evident  that  a  light  object  in  the  background,  as  a  white 
house  seen  against  dark  foliage,  must  be  much  more 
prominent  than  a  near  object,  seen  against  another  of  the 
same  color. 

In  general,  when  there  is  little  or  no  contrast  of  color, 
objects  are  difficult  to  see  without  regard  to  their  distance. 
Place  a  square  of  white  cardboard  in  front  of  a  larger 
square  of  the  same,  the  latter  coming  in  front  of  the 
blackboard.  The  smaller  can  be  seen  very  faintly.  In 
comparison  with  the  distinctness  with  which  the  larger  is 
seen  against  the  blackboard,  the  smaller  is  practically 
invisible.  This  experiment  proves  that  we  distinguish 
objects  through  contrasts  of  color,  and  we  have  to  con- 
sider w^hat  can  be  done  in  outline  simply,  to  render  the 
cfiect  of  Nature.  Can  no  more  be  done  than  to  repre- 
sent the  form  by  lines  of  uniform  strength? 

The  opinion  seems  to  be  general  that  more  can  be 
done.  We  find  that  instruction  is  often  given  to  repre- 
sent the  nearer  edges  by  strong  lines,  the  farther  ones  by 
light  lines ;  in  fact,  to  proportion  the  strength  of  the  line 
to  the  distance  of  the  part  it  represents.  Apply  this 
rule  to  the  representation  of  the  two  pieces  of  cardboard, 
and  the  nearer  is  accented  by  heavy  lines,  the  farther  by 
light  lines.     This  is  a  direct  contradiction  of  what  we  see, 


42  FREE-HAND  DRAWING. 

for  the  outline  of  the  nearer  is  barely  visible,  while  the 
farther  is  distinct  against  the  blackboard. 

In  color  we  certainly  should  not  think  of  representing 
the  nearer  as  darker  than  the  farther,  or  in  any  other 
way  than  as  it  appears,  and  the  same  is  true  of  light  and 
shade.  Why  should  we  not  do  the  same  when  possible, 
with  outline  ?  No  reason  to  the  contrary  can  be  given, 
for  the  difference  in  clearness  with  which  the  various 
lines  are  seen  is  the  result,  not  of  distance,  but  of  con- 
trasts of  color,  and  light  and  shade.  Of  course  we  shall 
expect  to  find  the  strongest  lines  among  the  nearest  ones, 
but  forther  than  this  we  cannot  go,  and  if  we  adopt  the 
conventional  accenting  recommended  by  text-books,  we 
are  working  by  rule  and  not  by  observation,  and  the  result 
will  be  the  production  of  hard,  mechanical  drawings. 

Character  appears  in  outlines.  An  object,  as  a  cast, 
having  a  smooth,  hard  surface  shows  these  qualities  in 
its  outlines,  which  will  be  represented  by  smooth  lines. 
A  cube  with  smooth  faces  has  sharp,  straight  edges,  which 
will  be  represented  by  straight  lines.  A  box  made  of 
rough  boards  has  broken  edges,  whose  character  may  be 
given  by  drawing  the  irregular  outline  in  which  one  sur- 
face breaks  into  the  other.  A  drawing  from  the  figure 
can  express  the  variations  in  the  appearance  of  the  out- 
lines, parts  of  which  are  sharp,  other  parts  blurred  by 
light  or  a  growth  of  hair. 

Light  affects  the  appearance  of  the  outlines  strongly. 


OUTLINE  DRAWING.  43 

in  some  places  making  them  distinct,  in  other  places 
indistinct.  An  even  line  for  everything  disregards  all 
these  variations  of  effect ;  so  also  does  any  conventional 
variation  of  strength.  If  the  student  is  allowed  to  disre- 
gard  effects  in  outline  work,  he  will  have  great  difficulty 
in  seeing  them  in  later  work.  There  is  no  more  labor 
involved  in  representing  effects  than  in  disregarding 
them,  for  one  line  is  as  easy  to  make  as  another,  o/'senui- 
tion  only  being  leqnited.  The  student  7<.>ho  can  see  can 
perform,  and  as  long  as  any  differences  can  be  found 
between  his  drawing  and  Nature,  he  can  learn  to  correct 
the  errors. 

The  conventional  accenting  taught  in  the  public  schools 
produces  the  most  mechanical,  hard,  and  unnatural 
sketches  when  the  student  works  from  Nature,  indoors  or 
out.  Undirected  he  would  never  produce  such  childish 
and  ridiculous  effects,  but  after  his  instniction  in  drawing 
from  the  object,  where  he  has  learned  that  lines  must  be 
represented  with  a  degree  of  strength  corresponding  to 
their  distance,  he  naturally  does  not  think  of  observing 
and  drawing  what  he  sees,  but  simply  mechanically 
grades  the  strength  of  line  as  he  has  lieen  taught.  He 
makes  the  heaviest  lines  of  the  drawing  where  there 
should  be  the  faintest  indications  of  lines,  and  often 
where  no  lines  at  all  would  be  better  than  faint  lines. 

It  is  almost  impossible  to  get  a  student  from  the  pub- 
lic schools  to  make  sketches  in  which  the  unimportant 


44  FREE-HAND  DRAWING. 

detail,  which  is  no  part  of  the  effect,  is  not  brought  out 
with  heavy  black  lines.  This  is  not  surprising,  for  he 
sees  this  detail  and  it  is  near  him,  therefore  according  to 
his  instruction  it  must  be  strongly  accented. 

In  outline,  as  in  other  mediums,  we  should  do  the  best 
we  can  to  express  what  is  before  us.  The  effect  of  the 
subject  should  be  considered  as  well  as  its  form.  There 
is  no  reason  why  the  student  should  not  be  taught  to 
observe  the  effect,  and  if  once  started  rightly  he  will 
advance  rapidly  and  will  make  drawings  which,  since 
they  are  representations  of  Nature,  will  have  variety  of 
effect,  will  be  true,  and  artistic. 

No  rule  can  be  given  other  than  to  study  and  represent 
simply  what  is  seen,  as  far  as  possible,  as  it  appears.  In 
outline,  without  any  light  and  shade,  it  is  impossible  to 
always  accent  the  lines  just  as  they  appear.  For  instance, 
some  edges  of  the  object  may  be  so  lost  in  the  shade  as 
to  be  wholly  invisible,  but  without  them  the  drawing 
might  be  incomplete  and  unsatisfactory.  A  correct 
impression  of  the  facts  must  be  conveyed.  No  important 
line  can  be  omitted  even  if  not  seen,  but  otherwise  the 
lines  should  be  represented  as  they  appear. 

In  drawings  of  the  geometric  solids,  where  there  are 
few  lines  in  nature,  it  will  sometimes  be  impossible  to 
accent  the  lines  as  they  appear,  for  some  of  the  most 
important  ones  may  be  invisible,  or  seen  so  faintly  that 
to  represent  them  as  they  appear  would  make  the  draw- 


OUTLINE  DRAWING.  45 

ing  give  a  false  impression.  Frequently  when  the  objects 
are  strongly  lighted  their  outlines  on  the  light  side  of  the 
group  intersect  one  another,  so  that  the  outline  of  the 
mass  is  composed  of  parts  of  those  of  several  objects. 
This  outline  is  very  prominent,  while  the  edges  inside 
the  outline  are  almost  lost  in  the  mass  of  light.  It  is 
evident  that  in  this  case  we  cannot  accent  as  we  see. 
We  must  accent  as  we  feel  the  group,  and  when  accent- 
ing as  the  lines  are  seen  is  unsatisfactory,  we  must  use 
our  judgment  and  make  the  accenting  express  the  facts 
in  a  satisfactory  manner. 

When  drawing  from  furniture  or  from  any  subject  hav- 
ing many  lines,  the  effect  will  generally  be  satisfactory 
when  the  lines  are  accented  as  they  are  seen.  Here 
there  are  so  many  lines  and  so  many  changes  in  direction 
that  the  parts  which  are  not  seen  will  rarely  be  missed, 
and  the  student  can  represent  more  nearly  what  he  sees. 
Rut  it  must  be  understood  that  it  is  wliolly  a  matter  of 
feeling  for  which  no  rule  can  be  given. 

At  first  most  students  will  have  difficulty  in  seeing  any 
difference  in  the  way  in  which  the  various  edges  appear. 
This  is  due  to  the  fact  that  but  a  single  point  can  be 
clearly  seen  at  any  one  time.  The  eye  glances  rapidly 
over  the  whole  of  an  object,  carefully  observing  all  its 
parts.  We  are  unconscious  of  this  motion.  All  parts  of 
the  object  are  seen  distinctly,  and  the  variety  of  effect  is 
not   realized.     All  the   parts  will   continue   to  give  the 


46  FREE-HAND  DRAWING. 

impression  of  equal  strength  until  the  abiUty  to  see  the 
whole  of  an  object  at  once  has  been  acquired,  as  explained 
on  page  t8.  It  is  not  possible  otherwise  to  see  simply, 
to  realize  effects  and  masses,  and  the  student  must  prac- 
tise until  he  can  thus  see  before  he  thinks  of  success  in 
any  medium,  for  all  demand  equally  a  study  of  the  com- 
parative strength  of  detail. 

Although  no  rule  for  accenting  can  be  given,  the  effect 
is  found  to  conform  to  the  principle  that  any  detail  ivhich 
co/nes  in  either  the  mass  of  the  li_s;ht  or  that  of  the  shade 
is  uninipoi-tant.  Thus  an  edge  defining  a  light  surface 
against  another  surface  also  light  is  not  prominent,  and 
an  edge  separating  a  surface  in  the  shade  from  another 
shade  surface  is  seen  faintly.  The  important  features 
are  those  which  come  between  the  light  and  the  shade. 


r 


CHAPTER   III. 
Interiors  and  General  Work. 

All  drawing,  whatever  the  subject,  should  be  carried 
on  in  the  same  way,  first  by  blocking  in  the  mass  of  the 
whole,  then  the  masses  of  the  various  parts,  the  detail 
coming  last  but  always  being  carefully  studied. 

In  drawing  from  objects  having  curved  lines,  the  stu- 
dent should  be  careful  not  to  be  content  with  the  gen- 
eral effect  of  the  line,  but  to  give  the  variations  from  the 
regular  curves  found  in  many  objects.  Thus  in  a  cast, 
lines  which  at  first  glance  seem  of  uniform  curvature  will 
be  found  to  be  composed  of  many  short,  flat  curves. 
Character  will  be  given  only  by  a  study  of  these  flat 
cur\es,  but  the  search  for  straight  lines  must  not  lead  to 
the  drawing  of  straight  lines  where  none  can  be  seen,  as 
in  an  ellipse. 

After  the  models,  common  objects  as  boxes,  furniture, 
etc.,  may  be  drawn.  These  may  be  arranged  in  groups 
and  an  idea  of  pleasing  composition  be  given.  This 
work  leads  directly  to  the  drawing  of  interiors.  No 
principles  other  than  those  explained  are  involved.  In 
this  work,  as  in  all,  the  aim  should  be  to  represent  as 

47 


48  FREE-HAA'D  DRAWING. 

nearly  as  possible  the  actual  appearance  of  everything. 
We  obtain  the  dimensions  of  this  appearance  on  a  plane 
which  is  perpendicular  to  the  direction  in  which  we  see 
the  object.  Carrying  out  this  principle  and  extending 
the  subject,  we  find  that  the  surface  which  gives  the 
appearance  is  that  of  a  sphere,  which  cannot  be  devel- 
oped. This,  then,  is  the  reason  why  we  cannot  always 
draw  just  what  we  see,  and  it  is  impossible  to  make  a 
sketch  which  shall  include  an  extended  range  of  vision, 
and  give  the  exact  appearance  of  each  part,  and  a  correct 
impression  of  the  whole  (pages  92,  93). 

The  space  which  can  be  included  in  a  model  drawing, 
and  which  may  be  represented  on  a  plane  without  notice- 
able distortion,  should  not  include  an  angle  at  the  eye  of 
over  twenty-eight  degrees.  If  this  is  much  exceeded 
the  questions  of  the  curvature  of  parallel  lines  for  both 
horizontal  and  vertical  distances  will  arise,  but  as  most 
drawings  require  a  larger  angle  the  question  must  be  con- 
sidered. 

The  mind,  knowing  lines  to  be  straight,  will  hesitate  to 
accept  their  representation  by  curved  lines,  or  knowing 
them  to  be  vertical,  will  not  readily  accept  their  repre- 
sentation by  inclined  lines.  The  drawing  should  give 
the  impression  of  Nature,  as  far  as  possible,  even  when 
the  eye  is  not  at  the  proper  distance.  The  impression 
of  vertical  lines  is  given  by  vertical  lines,  and  of  straight 
lines  by  straight  lines.      For  this  reason,  it  seems  best 


INTERIORS  AND    GENERAL    WORK.  49 

that  the  student  should  represent  what  he  sees,  as  nearly 
as  possible,  but  in  accordance  with  the  perspective  prin- 
ciple that  straight  lines  shall  be  represented  by  straight 
lines.  This  will  cause  him  to  represent  horizontal  lines 
which  extend  on  both  sides  by  parallel  horizontal  lines, 
and  to  substitute  for  the  curved  lines  found  in  objects  at 
angles  with  the  jiicture,  straight  lines  extending  to  two 
vanishing-points.  This  will  change  the  drawing  very 
little,  as  shown  on  plate  28. 

When  the  subject  is  extended  or  comes  very  near  the 
draughtsman,  causing  visual  angles  of  from  forty-five  to 
one  hundred  degrees  either  horizontally  or  vertically,  it 
is  evident  that  the  difference  between  the  appearance 
and  any  drawing  made  on  one  plane  will  be  very  marked, 
and  so.me  parts  of  the  drawing  must  be  quite  different 
from  the  actual  visual  angles  formed  in  the  eye.  This 
may  prevent  the  drawing  from  being  truthfully  blocked 
in  as  a  whole  at  first.  It  can,  however,  and  must  in  the 
beginning  be  placed  as  a  whole  approximately.  The 
central  part  or  the  most  important  portion  can  then  be 
drawn  as  it  appears.  The  proportions  of  the  outer  parts 
ran  be  referred  to  the  central,  and  the  distortion,  which 
is  inevitable  somewhere  in  an  extended  subject,  be  re- 
duced to  the  smallest  degree  by  making  the  perspective 
of  these  outer  and  less  important  parts  agree  with  that  of 
the  central  and  important  mass. 

The  different  parts  of  an  extended  subject   cannot  be 


50  FREE-HAND  DRAlVfNG. 

measured  or  compared  by  the  ordinary  use  of  the  pencil, 
for  its  distance  from  the  eye  changes  with  every  new  posi- 
tion. If  it  is  desired  to  compare  the  visual  proportions, 
the  pencil  must  be  held  at  one  distance  from  the  eye  by 
means  of  a  thread  attached  to  it  and  held  at  the  brow  by 
the  left  hand. 

When  it  becomes  necessary  to  make  a  perspective 
drawing  throughout,  as  sometimes  happens  when  three 
walls  of  a  room  are  to  be  shown,  the  proportions  of  this 
drawing  may  be  very  exactly  found  by  holding  the  pencil 
in  a  plane  parallel  to  the  end  of  the  room. 

This  drawing  should  be  avoided  when  possible  on 
account  of  the  serious  distortion  of  its  outer  parts,  and  it 
will  also  be  well  to  avoid  representing  one  side  of  a 
room  which  extends  far  on  both  sides  of  the  spectator. 
If  one  wall  is  to.be  represented,  it  is  better  to  draw  from 
one  end  of  the  room  than  from  the  centre,  as  the  lines 
will  vanish  and  the  distortion  be  less  marked.  When  two 
walls  are  represented,  the  lines  of  both  must  vanish. 
\\'hen  three  are  shown,  the  middle  one  must  have  no  van- 
ishing. Figure  9  shows  that  if  its  lines  vanish,  the  whole 
of  the  left  wall  will  be  outside  of  both  vanishing  points 
of  the  drawing,  and  thus  very  unpleasantly  distorted.  A 
(innving  should  never  extend  beyond  the  vanishing  points 
of  its  lines, 

A  very  slight  distance  may  be  represented  to  the  left  of 
the  left  point  in  Fig.  9,  when  the  drawing  represents  a 


LVTERIORS  AXD    GENERAL    WORK.  51 

court  or  any  interior  where  the  part  at  the  left  is  a  very 
unimportant  portion  of  the  drawing,  but  it  is  generally 
safer  to  end  the  drawing  at  the  vanishing  point. 

Distortion  such  as  that  in  Fig.  9,  is  seen  in  photographs 
taken  with  a  lens  of  wide  angle,  and  photographs,  the 
most  common  perspective  drawings,  exert  a  strong  influ- 
ence to  perpetuate  the  serious  distortions  in  the  drawings 
of  our  illustrators  and  artists. 

In  drawings  of  street  scenes,  etc.,  the  lines  are  long  and 
broken,  and  their  apparent  curvature  may  not  be  noticed 
if  each  part  is  drawn  as  it  appears.  In  such  subjects  one 
does  not  know  the  conditions.  The  lines  may  be  curved 
in  Nature.  Hence  there  is  not  the  instant  contradiction 
between  the  appearance  of  the  drawing  and  the  knowl- 
edge concerning  the  facts  of  the  things  represented.  If 
the  artist  chooses  sometimes  to  represent  straight  lines  by 
curved  Hnes,  he  has  Nature  as  authority  and  the  example 
of  noted  predecessors,  and  no  one  would  wish  to  say  that 
his  drawing  is  not  good  or  that  it  would  be  improved  by 
plane  perspective. 

In  interiors  and  in  street  scenes,  there  is  not  only  the 
question  of  horizontal  foreshortening  to  be  considered, 
but  also  that  of  vertical  foreshortening.  Whether  or  no 
this  foreshortening  shall  be  given  is  a  question  which  can 
■  be  answered  only  as  it  arises,  and  decided  according  to 
the  conditions  of  the  subject  and  the  aim  of  the  drawing. 
It  is  a  question  of  the  less  important  giving  way  to  the 


52  FREE-HAND  DRAIVIXG. 

more  important,  and  is  for  the  artist  rather  than  the  stu- 
dent, who  should,  until  he  has  attained  by  long  practice 
ability  to  judge  proportions  correctly,  never  be  permitted 
to  draw  other  than  those  he  sees. 

The  unnumbered  plates  following  are  from  students' 
drawings  from  Nature.  Such  work  should  be  the  aim  of 
drawing  in  the  public  schools,  whose  pupils,  taught  to 
observe  and  to  do  what  they  see,  may  make  a  great 
advance-in  this  direction. 

The  sketches  are  by  students  of  the  perspective  classes 
at  the  School  of  Drawing  and  Painting  of  the  Museum  of 
Fine  Arts,  and  at  the  Normal  Art  School.  They  illustrate 
the  beginning  and  the  end  of  a  course  in  model  drawing, 
which  is  the  only  perspective  necessary  to  the  artist. 


CHAPTER   IV. 
Drawing  in  the  Pubuc  Schools. 

The  value  of  a  course  in  drawing  when  the  subject  is 
properly  presented  can  hardly  be  overestimated,  but  it 
must  be  confessed  that  much  of  the  instruction  given  is 
such  that  its  benefit  is  a  matter  of  doubt. 

At  the  beginning  of  his  art  education,  the  pupil  should 
be  taught  to  see  correctly.  When  this  has  been  accom- 
plished, and  he  is  able  to  represent  truly  what  is  before 
him  as  it  appears,  and  not  as  he  thinks  he  sees  it,  then 
he  is  in  a  position  to  advance,  and  his  personality  may  be 
cultivated.  But  as  the  first  point  to  be  gained  is  ability 
to  see  truly,  it  follows  that  we  should  from  the  very  start 
demand  truth,  truth  of  outline,  truth  of  light  and  shade, 
and  truth  of  color. 

In  beginning,  I  wish  to  say  that  drawing  in  the  public 
schools  can  never  accomplish  results  of  any  value  until 
the  pupils  can  observe  for  themselves ;  in  other  words, 
until  they  can  draw  from  objects  instead  of  from  draw- 
ings. This  is  impossible  in  many  places  now  because  the 
teachers  have  not  materials.  The  schools  must  have 
models  and  all  necessary  materials,  or  the  work  will  be 

53 


54  FREE-HAND  DRAWING . 

simply  the  copying  of  drawings  in  the  books,  or  if  these 
are  not  used,  the  copying  of  theory  drawings  on  the 
board.  In  the  elementary  grades  the  instruction  can  be 
given  well  enough  in  the  classroom,  but  the  advanced 
grades  should  have  provided  for  them  a  room  arranged 
for  the  purpose.  Drawing  cannot  be  taught  without 
materials  any  more  than  manual  training  can  be  taught 
without  tools,  and  a  part  of  the  necessary  materials  can 
be  used  in  one  no  more  than  in  the  other. 

No  committee  wouUl  expect  a  boy  to  use  a  gouge  to  do 
the  work  of  a  chisel,  or  to  learn  to  use  his  tools  without 
wood,  or  that  a  class  should  get  along  with  tools  for  one 
student ;  yet  the  committee  or  superintendent  often  ex- 
pects drawing  to  be  taught  without  materials,  or  with  ma- 
terials for  part  of  the  class. 

In  most  public  schools  attention  is  now  given  to  draw- 
ing. In  cities  this  instruction  is  generally  in  charge  of  a 
special  teacher,  but  this  special  teacher  can  do  little  more 
than  to  direct  the  regular  teachers.  The  subject  is  com- 
paratively new,  these  teachers  have  had  perhaps  no  regu- 
lar instruction  in  drawing,  and  few  have  had  the  liking 
for  the  subject  necessary  to  interest  them  in  the  work,  or 
to  cause  them  to  obtain  the  knowledge  they  are  expected 
to  impart,  and  with  all  the  stress  of  work  upon  them,  it  is 
surprising  that  they  have  accon^jplished  as  much  as  has 
been  done  in  some  places.  In  many  cases  the  special 
teachers  have  had  but  little  training,  and  frequently  this 


DRAWING   IN   THE   PUBLIC   SCHOOLS.  55 

has  been  simply  in  the  direction  of  understanding  the 
course  of  work  laid  out  in  drawing-books,  or  of  studying 
the  "  best  methods  "  instead  of  acquiring  some  practical 
ability  in  drawing.  This  has  been  the  inevitable  result 
of  the  rapid  growth  of  the  subject,  and  years  must  pass 
before  it  will  be  understood  in  all  its  bearings,  and  before 
there  will  be  special  instructors  who  have  had  the  training 
requisite  to  success. 

The  aim  of  drawing  in  the  public  schools  should  be 
educational,  and  not  specialistic.  The  pupils  cannot  all 
be  artists  or  designers,  or  engineers,  but  all  will  be  bene- 
fited by  a  logical  course  in  drawing,  and  if  they  have  it, 
discover  special  talent,  which  may  be  developed  in  the 
higher  schools.  The  instruction  in  free-hand  drawing  can 
be  practical  and  give  to  all  right  ideas,  and  to  almost  all 
ability  to  sketch  from  Nature  with  a  degree  of  freedom 
and  truth.  The  public  school  instruction  can  be  such 
that  the  student  who  wishes  to  study  art  upon  leaving 
school  may  do  so  with  a  good  foundation  and  nothing  to 
unlearn 

The  instruction  in  pictorial  drawing  is  now  the  weak- 
est part  of  the  work  in  the  pubhc  schools.  It  is  so  be- 
cause it  is  neglected,  or  because  bad  methods  are  used. 
At  the  present  time  instruction  in  drawing  in  many  places 
is  largely  instruction  in  manual  training  and  kihdergarten 
work.  Without  doubt  this  ij  valuable,  but  not  as  draw- 
ing, and  it  should  not  take  the  place  of  drawing.     Draw- 


56  FREE-HAND  DRAWING. 

ing  should  have  an  hour  by  itself.  Cutting  paper,  whit- 
thng  paper-knives,  sewing  pen-wipers,  etc.,  can  never  give 
the  least  ability  in  drawing ;  neither  can  this  work,  as 
many  carry  it  on,  give  any  knowledge  of  working  draw- 
ings. The  making  of  objects  can  be  of  great  assistance, 
and  should  naturally  go  with  the  study  of  working  draw- 
ings, but  the  objects  should  be  made  from  the  drawings 
which  must  show  all  the  construction. 

I  do  not  see  how  the  making  of  objects  can  be  done  in 
school  without  special  time  being  given  to  it,  and  the 
subject  of  drawing  proper  not  suffer ;  and  it  seems  that 
as  the  result  in  many  places  of  the  present  agitation  in 
favor  of  manual  training,  this  subject  takes  the  place  of 
drawing.  Many  drawing  teachers  are  unconsciously 
effecting  this  by  placing  in  their  course  paper-cutting 
and  the  making  of  objects  that  have  no  connection  with 
either  the  free-hand  or  the  instrumental  drawing. 

In  many  cities  drawing-books  are  used.  These  books 
contain  examples  of  historic  ornament  and  design  which 
are  to  be  copied,  and  also  drawings  of  models  and  com- 
mon objects,  some  of  which  are  to  be  copied,  and  others 
are  given  as  illustrations  of  possible  appearances. 

In  many  places  most  if  not  all  of  the  work  in  object 
drawing  is  thus  copying,  and  so  little  of  actual  drawing 
from  the  objects  is  done,  that  with  the  objects  before 
them  students  are  found  copying  the  drawing  of  the 
student  in  front,  and  the  drawings  of  a  whole  row  are 


DRAWING  IN   THE  PUBLIC  SCHOOLS.  57 

alike  ;  or  copying  the  drawing  made  upon  the  board  to 
illustrate  the  principles.  We  have  even  known  of  cases 
where  the  pupil  has  turned  to  some  text-book,  as  a  geom- 
etry, in  which  he  has  tried  to  find  the  appearance  of  the 
object  before  him.  Such  are  the  results  which  come 
from  copying  drawings. 

It  is  easier  for  the  teacher  to  allow  the  pupil  to  copy, 
but  such  work  is  of  no  value,  and  the  copies,  even  if 
neatly  done,  deserve  only  censure.  The  few  teachers 
who  have  had  the  courage  to  dispense  with  copies  deserve 
praise  for  showing  that  drawing  can  be  taught  from  the 
objects,  and  their  example  should  result  in  a  general 
change  from  books  to  Nature.  In  many  places  it  is  pos- 
sible that  nothing  could  be  done  in  drawing  were  it  not 
for  the  books.  Rightly  used,  they  may  be  of  assistance, 
but  the  pictorial  drawing  should  be  by  itself  in  a  blank 
book,  and  each  drawing  should  be  made  from  the  object. 

The  change  from  copying  to  drawing  from  the  object 
will  require  hard  work  from  both  pupil  and  teacher,  and 
at  first  the  drawings  will  be  very  unsatisfactory  in  them- 
selves ;  but  after  a  short  time,  when  the  pupils  have  been 
started  rightly  in  the  lower  grades,  they  will  draw  readily 
and  with  greater  freedom,  and  will  be  able  to  draw  from 
Nature,  which  they  never  are  under  the  present  systems 
that  allow  them  to  copy  from  a  book  or  the  board. 

We  have  advised  that  art  students  draw  with  charcoal 
and  in  light  and  shade  at  once.     Charcoal  is  not  suited 


58  FUEE-IIAND  DRAWING. 

to  public  school  work,  at  least  not  in  the  lower  grades, 
where  it  becomes  a  question  of  outline  in  pencil. 

At  present  it  is  the  aim  of  most  courses  in  drawing  to 
give  a  thorough  knowledge  of  the  actual  form  before 
attempting  to  represent  its  appearance.  The  knowledge 
of  the  facts  is  of  course  of  some  assistance  to  the  person 
who  is  to  represent  them.  A  glance  at  the  object  and  it 
is  recognized,  and  the  mind  supplies  the  information 
which  it  might  take  the  eye  some  time  to  discover.  But 
this  knowledge  is  more  apt  to  do  harm  than  good,  for 
the  pupil  uses  it  instead  of  his  eyes.  For  this  reason,  I 
should  advis<.  that  the  continued  and  thorough  study  of 
facts,  now  followed  by  most  teachers,  be  postponed  until 
the  pupils  have  had  some  practice  in  representing  the 
facts,  or  at  least  that  the  study  of  the  appearance  begin 
with  the  study  of  the  facts. 

The  facts  can  be  taught  perfectly  in  a  very  short  time, 
but  to  attain  perfection  in  their  representation  is  a  prob- 
lem requiring  much  more  study  and  long  continued  effort, 
and  for  this  reason  it  should  be  given  earlier  and  more 
serious  attention. 

The  study  of  appearances  in  the  lower  grades  may 
begin  with  plane  figures  cut  from  cardboard  or  paper,  as 
the  square,  circle,  triangle,  hexagon,  etc.  These  may  be 
placed  horizontal  upon  the  desk  and  their  appearances 
studied.  This  involves  the  use  of  the  pencil  in  measur- 
ing, and  it  must  also  be  held  horizontal  to  assist  the  pupil 


DRAWING  IN  THE  PUBLIC  SCHOOLS.  59 

to  see  the  angles  of  the  Hnes.  In  beginning,  this  work 
may  be  made  easy  by  placing  the  card  in  the  centre  of 
the  desk,  when  the  lines  of  the  desk  serve  for  horizontal 
comparison. 

The  cards  may  be  of  such  dimensions  that  the  draw- 
ings can  be  made  the  size  of  the  cards.  The  measure- 
ment of  height  will  then  be  obtained  by  placing  the  lower 
end  of  the  pencil  at  the  nearest  point  or  side  of  the  card, 
and  the  thumb-nail  to  cover  tl»e  farther  angle  or  edge  of 
the  card.  This  gives  the  exact  height  of  the  drawing. 
It  is  thought  that  this  use  of  the  pencil  in  determining 
proportions  will  be  readily  understood.  The  pencil 
should  of  course  be  about  vertical,  but  to  be  exact  it 
should  tip  back  slightly. 

When  the  card  has  its  nearest  edge  parallel  to  the 
desk  line,  the  width  of  the  drawing  will  be  the  length  of 
this  edge.  If  the  edge  is  not  parallel  to  the  desk,  its 
length  will  be  measured  on  the  pencil  by  placing  the 
pencil  parallel  to  the  edge  of  the  desk  and  touching  the 
nearest  end  of  the  line,  whose  apparent  length  will  be  to 
the  point  just  under  the  farther  end,  or  to  where  a  verti- 
cal pencil  covering  the  farther  point  will  meet  the  hori- 
zontal pencil.  This  way  of  measuring  will  give  very  good 
results,  but  before  measuring  any  except  the  nearest  edge, 
the  drawing  should  be  made  by  the  eye  alone. 

It  will  be  well  to  draw  the  cards  at  different  levels. 
This  may  be  done  by  placing  them  on  boxes  or  books. 


60  FREE-HAND  DRAWING. 

By  holding  them  horizontal  and  on  the  level  of  tlie  eye, 
the  pupil  will  see  that  they  all  appear  horizontal  lines, 
and  that  their  forms  are  seen  only  when  they  are  above 
or  below  this  level. 

I  should  not  attempt  to  teach  much  perspective  theory. 
Until  the  pupils  are  older,  practice  alone  is  what  they 
need.  They  can  see  that  the  apparent  heights  of  the 
figures  decrease  as  the  planes  are  brought  toward  the 
level  of  the  eye,  at  which  all  appear  lines.  They  can 
also  discover  that  parallel  retreating  edges  appear  to 
converge.  This  may  be  seen  by  placing  two  pencils 
together,  and  then  separating  them  until  each  appears 
to  coincide  with  an  edge.  The  pencils  must  of  course 
be  held  at  right  angles  to  the  direction  in  which  the 
object  is  seen. 

The  cards  may  be  held  in  a  vertical  position  by  a  small 
block  of  wood,  to  which  they  may  be  fastened  by  a  tack. 
In  this  position  the  height  will  be  the  greatest  dimension, 
but  the  proportions  will  be  obtained  as  before.  Tlie 
positions  of  the  cards  being  changed  for  each  lesson,  in 
a  short  time  the  pupils  will  learn  to  use  their  eyes  and 
will  draw  the  cards  fairly  well. 

Both  horizontal  and  vertical  positions  of  the  cards  may 
be  studied  in  the  same  lesson  by  folding  a  rectangular 
card  so  that  a  right  angle  is  formed,  one  part  being  hori- 
zontal and  the  other  vertical,  and  held  at  right  angles  by 
being  tacked  to  a  small  piece  of  wood.  Other  forms 
may  be  studied  in  the  same  way. 


DRAWING  IN   THE  PUBLIC  SCHOOLS.  61 

When  able  to  draw  the  cards  from  the  position  directly 
in  front,  the  next  step  is  to  draw  them  when  at  the  right 
or  left.  To  do  this,  each  pupil  may  draw  from  a  card 
placed  near  the  corner  of  his  desk  or  on  the  desk  at  his 
side.  This  is  much  more  difficult  than  to  draw  from  the 
card  placed  on  the  centre  of  his  own  desk.  The  ten- 
dency will  be  to  think  of  the  line  of  the  desk  as  appear- 
ing horizontal,  when  in  this  case  it  appears  to  vanish. 
For  this  work  the  pupil  must  learn  to  hold  the  pencil 
horizontal,  and  at  right  angles  to  the  direction  in  which 
he  sees  the  card.  As  this  position  of  the  card  involves, 
beside  this  difficult  test,  the  comparison  of  height  and 
width  on  the  pencil,  it  may  be  found  necessary  to  post- 
pone the  work  until  the  pupil  has  had  practice  in  draw- 
ing from  objects  placed  in  front  of  him.  It  will  be  well 
to  advance  the  work  as  rapidly  as  possible.  Tlie  teacher 
should  have  little  trouble  in  showing  that  the  work  is  nec- 
essary and  the  beginning  of  pictorial  drawing,  and  if 
properly  presented,  the  pupils  will  be  interested.  The 
more  the  drawing  seems  in  itself  a  picture  and  not  a  dia- 
gram, the  more  interested  will  they  be. 

A  simple  preparation  for  the  subject  of  model  drawing 
from  the  solid  blocks  may  be  given  by  drawing  from  two 
planes,  so  placed  as  to  represent  the  bxses  or  ends  of  the 
various  prisms.  Thus  two  squares  may  be  fastened  by  a 
tack  through  their  centres  to  a  small  cylinder  of  wood, 
which  represents  the  axis  of  the  prism.     The  prism  thus 


62  FREE-IIAXD  DRAWING. 

represented  may  be  placed  vertical  or  horizontal.  As  all 
the  edges  of  each  card  are  seen,  this  practice  will  help 
the  pupil  when  he  draws  from  a  solid,  in  which  all  the 
edges  are  not  seen. 

A  better  arrangement  is  a  skeleton  frame  in  which  the 
edges  are  represented  by  wires,  or  in  which  wires  con- 
nect the  bases  of  the  object,  which  are  sheets  of  tin. 
Drawing  from  these  objects  will  be  interesting  and  prac- 
tical. 

After  this  work  the  solids  may  be  studied  in  whatever 
order  seems  best.  If  the  pupil  has  learned  to  use  his 
eyes,  there  is  little  choice  as  to  the  order,  and  by  the 
time  he  is  ready  for  the  high  school  he  should  be  able 
to  draw  the  common  forms  quickly  and  truthfully,  not 
only  singly,  but  in  groups. 

The  best  and  cheapest  way  to  teach  model  drawing  is 
by  the  use  of  a  slate  of  glass  on  which  the  drawing  is 
made  with  a  pencil  prepared  for  the  purpose,  and  erased 
when  finished.  If  drawings  are  made  in  this  way,  they 
can  be  instantly  tested  by  holding  the  slate  in  front  of 
the  object  so  that  the  lines  upon  the  slate  appear  to 
cover  the  edges  of  the  object,  the  drawing  being  of  such 
size  that  the  slate  may  be  held  in  the  hand  to  apply  the 
test.  If  the  objects  are  large,  they  should  be  placed  far 
enough  away  to  have  the  drawing  upon  the  slate  come  of 
the  right  size.  The  easiest  way  is  to  have  the  pupils 
draw  from  small  objects  on  their  own  desks.     When  the 


DRAWING  IN   THE  PUBLIC  SCHOOLS.  63 

drawing  is  to  be  tested,  the  slate  can  rest  upon  the  desk 
or  be  steadied  by  the  hand. 

As  an  objection  to  the  use  of  this  slate,  it  could  be  said 
that  some  might  trace  the  appearance  witliout  previous 
drawing,  but  this  would  not  in  itself  be  harmful,  for  it 
would  simply  decrease  the  value  derived  from  the  lesson 
by  drawing  first  by  the  eye  alone. 

\\'hen  the  drawing  on  this  transparent  slate  has  been 
carried  as  far  as  the  pupil  can  see,  he  may  instantly  test 
it  by  holding  it  in  front  of  the  object.  If  correct,  the 
lines  of  the  drawing  will  apjiear  to  cover  the  edges  of  the 
object ;  if  not  correct,  the  inaccuracies  can  be  noted  and 
a  second  attempt  made. 

The  cost  of  the  glass  will  be  equalled  in  a  short  time 
by  that  of  the  paper  saved  by  its  use.  I  am  confident 
that  the  slate  used  in  this  manner  will  in  a  short  time 
give  the  average  pupil  of  even  the  lower  grades  more 
ability  in  drawing  than  he  now  obtains  by  his  entire 
public  school  training.  This  method  will  make  drawing 
easier  and  more  interesting,  and  will  enable  all  the  teach- 
ers, without  special  exertion,  to  make  drawing  of  some 
value. 

The  drawing  lesson  vnW  certainly  be  easier  for  the 
teacher  than  now,  for  the  drawings  will  test  themselves, 
and  teachers  who  cannot  draw  may  obtain  good  results. 
I  do  not  mean  that  teachers  can  get  along  without  being 
able  to  draw,  for  drawings  on  paper  must  be  made  and. 


6+  FREE-HAND  DRAWING. 

corrected,  but  I  think  the  glass  will  be  of  very  great  value, 
especially  when  teachers  are  not  thoroughly  prepared. 

It  is  thought  that  this  use  of  the  slate  will  prove  inter- 
esting to  the  pupils,  but  if  it  is  found  that  they  do  not 
apply  themselves  to  the  work,  thinking  that  a  slate  is  too 
childish,  it  may  be  used  at  first  as  in  the  later  work,  in 
connection  with  the  use  of  paper.  The  drawing  may  be 
made  by  eye  alone,  first  on  the  slate  or  on  the  paper,  as 
is  preferred.  In  whatever  way  the  work  is  carried  on, 
the  use  of  the  slate  gives  an  easy  and  sure  test  of  the 
accuracy  of  the  proportions,  and  for  this  purpose  the 
slate  may  be  used  to  great  advantage  through  the  work 
of  all  the  grades  and  the  high  school. 

An  improvement  on  the  simple  frame  is  the  attachment 
at  each  side  of  wires  fitting  in  the  frame  so  as  to  be  drawn 
out  to  any  length,  the  desk  having  two  holes  made  to 
receive  the  wires.  By  means  of  these  wires  the  slate 
with  the  drawing  may  be  held  perfectly  steady,  thus 
allowing  the  exact  comparison  of  the  drawing  with  the 
object.  Of  course  the  eye  must  be  held  in  one  place  for 
this  comparison. 

By  means  of  this  slate,  any  teacher  can  quickly  obtain 
all  the  practice  necessary  to  make  up  for  lack  of  training 
in  drawing,  and  if  the  slate  is  properly  used,  the  drawing 
always  being  made  by  eye  before  holding  the  glass  slate 
in  front  of  the  object,  it  will  be  of  great  assistance  to  all 
who  wish  to  learn  to  draw. 


DRAWING  IN   THE  PUBLIC  SCHOOLS.  65 

When  the  pupil  can  draw  the  simple  objects,  there  is  no 
reason  why  the  light  and  shade  may  not  be  represented 
by  pencil  tints  put  on  with  the  side  of  the  pencil ;  in  the 
advanced  grades  charcoal  can  be  used. 

The  high  school  work  should  include  furniture  draw- 
ing, and  corners  of  the  room,  with  more  difficult  groups  of 
models.  A  graduate  of  this  school  should  certainly  have 
the  ability  to  sketch  indoors  and  out,  with  truth  so  far  as 
proportion  is  concerned.  It  is  hoped  that  the  importance 
of  this  subject  may  be  realized,  and  that,  if  necessary, 
some  of  the  less  important  work  may  give  way  that  this 
may  improve. 

Much  help  will  be  obtained  from  examples  of  good 
drawings  by  advanced  students  and  illustrators.  With 
very  small  outlay  each  teacher  can  procure  from  maga- 
zines and  papers  reproductions  of  pencil,  pen  and  ink, 
and  shaded  drawings  by  the  best  artists.  If  these  repro- 
ductions are  placed  where  they  can  be  seen  all  the  time, 
they  will  interest  the  pupils,  and  give  them  an  idea  of 
expression  such  as  they  can  never  obtain  from  the  mechan- 
ical cuts  of  most  drawing-books.  Care  should  be  taken 
to  secure  some  drawings  simple  in  character,  which  may 
serve  to  interest  the  pupil  in  his  own  elementary  work. 

These  drawings  should  not  be  copied,  for  if  copying  is 
begun,  it  is  almost  certain  to  be  done  to  excess,  and  as 
has  been  said,  the  elementary  work  of  the  public  schools 
cannot  properly  consider  technique.     It   is  hoped  that 


66  FREE-HAND  DRAWING. 

soon  the  teachers  who  are  now  talking  about  methods, 
etc.,  may  give  their  attention  to  the  simple  study  of 
Nature,  and  the  making  of  truthful  drawings. 

Some  have  attempted  to  state  theories  of  color  and 
aesthetics,  which  the  student  may  study  to  improve  his 
taste.  The  value  of  this  theory  may  be  illustrated  by 
referring  to  the  numerous  statements  of  perspective  prin- 
ciples which  have  been  drilled  into  the  students  of  many 
schools,  who  are  at  the  present  time  making  the  fearful 
and  wonderful  productions  labelled  "  from  the  object." 

The  most  practical  solution  of  this  problem  has  been 
given  by  an  artist,  who  in  one  of  the  schools  of  Salem, 
Mass.,  has  just  arranged  pictures  by  good  artists,  photo- 
graphs, casts,  and  otlier  reproductions  of  the  best  art 
work.  The  influence  of  good  examples  of  this  nature 
cannot  fail  to  cultivate  the  taste  and  raise  the  artistic 
standard  of  the  people.  The  time  given  to  theories  of 
the  beautiful  will  be  much  better  spent  in  the  study  of 
Nature  involved  in  the  simplest  drawing. 


CHAPTER   V. 
Tests. 

Paragraphs  marked  (T.)  are  for  the  use  of  teachers  only. 

In  beginning,  the  student  should  understand  that  his 
drawings  are  of  no  value  in  themselves,  but  are  of  use  only 
as  they  train  the  eye  to  see  correctly.  The  eye  can  be 
taught,  or  rather  the  mind  can  be  made  to  accept  the 
image  of  the  eye,  only  by  depending  upon  it,  and  if  the 
student  begins  by  measuring  and  testing  he  will  never  be 
able  to  draw  othenvise.  This  is  undesirable  for  many 
reasons,  the  most  important  being  that  no  measurements 
can  be  applied  which  will  take  the  place  of  correct  per- 
ception, or  begin  to  equal  the  trained  eye.  It  is  thus 
important  that  the  student,  from  the  beginning,  depend 
entirely  for  his  first  drawing  upon  his  eyes. 

The  best  possible  training  for  all  young  or  old  is  the 
use  of  the  glass,  explained  on  page  62.  Any  one  who 
wishes  to  train  his  eyes  to  correct  seeing  can  do  so  most 
quickly  by  drawing  with  the  special  pencil  upon  this  slate 
by  eye  alone,  his  impressions  of  the  form,  and  then  testing 
the  drawing  by  holding  it  in  front  of  the  object. 

The  readiest  way  of  determining  the  apparent  propor- 
tions of  an  object  is  by  the  use  of  a  pencil  or  any  straight, 

67 


68  FREE-HAND  DRAWING. 

slender  rod  held  at  arm's  length,  and  to  appear  to  cover 
the  lines  to  be  compared.  Thus  the  end  of  the  pencil  rV, 
may  be  held  so  as  to  appear  to  cover  the  top  of  an 
object,  whose  apparent  height  may  be  measured  on  the 
pencil  by  means  of  the  thumb-nail  placed  so  as  to  appear 
to  cover  the  bottom  of  the  object.  If  the  pencil  is  now 
turned  into  a  horizontal  position,  the  apparent  height  of 
the  object  may  be  compared  with  its  apparent  width.  If 
the  measurement  covering  the  height  is  one-half  the  dis- 
tance on  the  pencil  which  covers  the  width,  the  group 
appears  twice  as  wide  as  high.  In  this  way  the  apparent 
proportions  of  any  object  or  group  may  be  found. 

It  is  important  that  this  use  of  the  pencil  shall  deter- 
mine simply  the  proportion  of  the  drawing  and  not  its 
actual  size.  The  measurements  on  the  pencil  must  not 
be  transferred  to  the  paper,  for  the  eye  and  hand  are  in 
different  positions  when  the  various  measurements  are 
taken,  and  if  they  are  transferred  to  the  paper  the  draw- 
ing resulting  will  be  incorrect  in  proportion. 

The  slightest  change  in  distance  of  the  pencil  from  the 
eye  when  proportions  are  compared  will  occasion  inac- 
curacy. The  only  way  to  be  at  all  correct  is  to  hold  the 
pencil  as  far  from  the  eye  as  possible,  the  arm  being  ])er- 
fectly  straight  and  the  pencil  being  turned  by  twisting  the 
entire-  arm. 

The  pencil  must  be  at  right  angles  to  the  direction  in 
which  the  object  is  seen.     Nearly  all  students  think  the 


TESTS.  69 

pencil  should  be  parallel  to  the  side  of  the  room,  or  the 
bench  upon  which  the  object  rests.  This,  however,  is 
wholly  false,  for  the  position  of  the  object  with  reference 
to  its  surroundings  is  of  no  consequence,  and  must  not 
be  considered  when  the  actual  appearance  of  the  object 
is  desired.  If  a  cube  is  to  be  represented,  the  student 
must  look  at  it,  and  the  plane  which  gives  its  real  appear- 
ance is  perpendicular  to  the  direction  in  which  he  looks, 
and  when  measuring,  the  pencil  must  always  be  held  in 
this  position.  When  thus  held,  its  ends  are  the  same 
distance  from  the  eye. 

A  good  plan  is  to  find  some  position  in  the  fingers  in 
which    the    pencil   is   perpendicular   to  the  arm,  which      /-  ///^ 
when  outstretched,  brings  the  pencil  into  practically  the 
correct  position.  Fig.  lo. 

(T.)  Jn  the  public  schools  when  the  subject  is  begun, 
some  may  find  that  a  pin  pushed  into  the  pencil  at  right 
angles  to  it  will  help  to  place  the  pencil.  When  the  pencil 
is  held  so  that  only  the  head  of  the  pin  is  seen,  the  pen- 
cil is  perpendicular  to  the  direction  in  which  the  pupil 
looks.  A  better  device  may  be  made  by  bending  a  piece 
of  soft  wire  (a  hair-pin)  about  a  large  knitting-needle  as 
shown  in  Fig.  12.  One  end  of  the  wire  projects  at  right 
angles  to  the  needle,  and  the  other  extends  back  and 
projects  a  short  distance  perpendicular  to  the  first  end. 
The  longer  end  serves  as  a  sight  to  place  the  needle  cor- 
rectly.    The  ware  should   press   the  needle  enough   to 


70  FREE-HAND  DRAWING. 

keep  in  place  upon  it.  It  may  be  moved  by  the  finger 
or  thumb,  and  the  measurement  taken  by  sighting  over 
the  short  end.  This  sUde  will  assist  greatly,  and  as  it  is 
important  that  measurements  should  be  correct,  it  is 
advised  that  every  student  who  cannot  hold  the  pencil 
properly  be  provided  with  this  measuring-needle  and 
slide.  It  will  also  assist  when  one  measurement  is  not  an 
easily  determined  part  of  the  other.     See  page  23. 

(T.)  The  smaller  measurement  should  always  be  com- 
pared with  the  larger.  If  the  former  is  one-half  or  one- 
third  of  the  latter,  this  is  easily  determined,  but  if  the  first 
is  three-fifths  or  four-ninths  of  the  second,  the  proportion 
is  not  so  easy  to  determine,  and  if  the  two  measurements 
can  be  taken  in  such  a  way  that  they  may  be  compared 
at  leisure^  the  proportion  may  be  more  surely  determined. 
This  may  be  done  by  taking  the  smaller  by  the  sliding 
wire  and  the  larger  by  the  thumb. 

If  the  back  end  of  the  pencil  is  used  to  measure  by, 
the  pencil  will  be  held  correctly  when  the  end  appears  a 
straight  line,  thus  producing  the  same  result  as  the  pin 
projecting  from  the  pencil. 

The  distance  of  the  needle  or  pencil  from  the  eye 
when  proportions  are  compared  must  be  the  same.  The 
distance  is  so  apt  to  vary  that  unless  each  comparison  is 
made  several  times  with  the  same  result,  there  is  little 
chance  of  the  measurements  being  correct.  It  is  useless 
to  think  that  tests  not  carefully  taken  are  worth  the  time 


TESTS.  71 

given  them.  It  is  much  better  to  take  the  one  proportion 
of  height  and  width  carefully,  than  to  spend  the  time 
necessary  to  do  this  on  half  a  dozen  measurements  which 
are  sure  to  contradict,  and  do  more  harm  than  good. 

It  is  impossible  to  compare  accurately  a  short  distance 
with  a  long.  If  the  height  is  equal  to  or  nearly  one-half 
or  one-third  the  width,  care  will  so  determine  it,  but  with 
every  new  position  of  the  hand  in  moving  a  short  dis- 
tance over  a  long  inaccuracy  arises,  and  it  is  well  to 
avoid  such  comparisons. 

The  inaccuracy  is  produced  by  inability  to  hold  the 
pencil  at  exactly  the  right  place,  and  also  by  the  change 
in  the  distance  of  the  pencil  which  every  movement 
away  from  the  first  ix)sition  occasions. 

This  movement  may  be  realized  by  tying  a  thread  to 
the  pencil  and  measuring  its  distance  from  the  eye  by 
holding  the  thread  with  the  left  hand  against  the  brow. 
If  the  arm  is  dropped  for  the  measurement  of  a  near 
object  and  the  thread  is  tight,  it  will  loosen  when  the  arm 
is  raised,  and  in  the  same  way  it  will  change  for  horizon- 
tal movement.  The  only  way  in  which  exact  measure- 
ments of  an  extended  subject  can  be  taken  is  by  the  use 
of  such  a  measuring-thread  for  the  pencil ;  but  we  wish 
to  simplify  the  subject  as  much  as  possible,  and  if  reason- 
able care  is  exercised  the  variation  in  the  distance  of  the 
pencil  may  be  made  so  slight  as  to  be  unimportant  in 
the  drawing  of  small  objects. 


72  FREE-HAXD   DRAWING. 

When  possible,  all  comparisons  should  be  made  by 
swinging  the  pencil  from  a  vertical  into  a  horizontal  posi- 
tion, by  motion  of  the  whole  arm  from  the  shoulder,  and 
avoiding  change  in  distance  by  revolving  the  pencil 
about  one  end  of  the  first  measurement.  Thus  if  the 
height  and  width  of  a  table  are  to  be  compared,  instead 
of  measuring  the  width  along  the  top  and  dropping  the 
hand  to  compare  the  width  with  the  height,  or  measuring 
the  height  and  then  lifting  the  hand  to  compare  with  the 
width,  make  the  comparison  by  taking  the  width  along 
the  top,  and  swinging  the  pencil  down  about  the  thumb  ; 
or  by  taking  the  width  at  the  bottom  and  swinging  the 
pencil  up  about  the  thumb,  as  in  Fig.  13.  Measuring  in 
this  way  will  assist  greatly  to  correct  results. 

(T.)  A  short  distance  may  of  course  be  compared  with 
a  long,  with  a  degree  of  accuracy  varying  with  the  student ; 
but  such  measurements  are  not  recommended  and  are 
umiecessary,  as  other  tests  will  give  better  results. 
Another  way  by  which  distances  may  be  compared  is  by 
marking  upon  the  edge  of  a  ruler  or  piece  of  cardboard 
with  a  pencil.  The  distances  may  be  compared  at 
leisure. 

The  above  are  the  direct  tests  for  proportion,  and  if 
carefully  taken,  should  give  the  correct  mass  of  the  draw- 
ing, but  for  smaller  proportions  and  directions  of  lines 
other  tests  are  better. 

The  lilies  with  which  it  is  natural  to  compare  directions 


TESTS.  73 

are  vertical  and  horizontal  lines.  A  horizontal  line 
whose  ends  are  equi-distant  from  the  eye  appears  hori- 
zontal and  is  represented  by  a  horizontal  line.  A  verti- 
cal  line  appears  vertical  and  is  always  represented  by  a 
vertical  line.  If  a  ruler  is  held  horizontal,  with  its  ends 
equally  distant  from  the  eye,  it  illustrates  the  appearance 
represented  by  a  horizontal  line  in  the  drawing.  By 
looking  over  the  ruler  thus  held,  the  apparent  directions 
of  lines  of  the  object  may  be  compared  with  the  horizon- 
tal. 

A  threatl  with  a  weight  attached  serves  as  a  plumb- 
line.  By  hokling  it  in  front  of  the  object  its  lines  may 
be  compared  with  the  vertical.  The  thread  is  often  bet- 
ter than  the  ruler  or  pencil  for  the  horizontal  line,  as  it 
hides  none  of  the  object.  Care  must  always  be  taken  to 
hold  the  thread  perpendicular  to  the  line  of  sight.  This 
position  is  easiest  obtained  by  directly  facing  the  group, 
extending  the  arms  ecpially,  and  holding  about  two  feet 
of  the  thread,  whose  ends  are  then  equally  distant  from 
the  eye. 

More  care  must  be  exercised  to  have  the  thread  hori- 
zontal. This  position  can  be  obtained  only  by  seeing 
nothing  but  the  thread  until  it  is  levelled,  when  the  stu- 
dent may  look  behind  it.  If  the  student  sees  the  group 
b-jfore  the  thread  is  level,  its  lines  will  probably  make  the 
thread  seem  horizontal  when  it  is  not.  If  there  are  hori- 
zontal lines  in  the  subject  which  are  parallel  to  the  pic- 


6 


74  FKEE-UAND  DRAWING. 

ture  ("  not  foreshortened  "),  they  will  appear  horizontal 
and  will  place  the  thread  correctly ;  but  if  the  horizontal 
lines  of  the  subject  are  not  thus  situated,  they  will  not 
appear  horizontal,  and  so  will  cause  the  thread  to  be  out 
of  level. 

It  may  seem  that  unnecessary  space  has  been  given  to 
these  directions,  but  it  has  been  found  almost  impossible 
to  make  many  students  understand  the  matter,  and  hold 
the  thread  correctly,  even  after  repeated  explanations 
and  illustrations.  Some,  after  months  of  study,  are 
found  holding  the  thread  or  pencil  at  an  angle  of  from 
ten  to  thirty  degrees  away  from  the  correct  position,  and 
it  is  thought  that  no  explanation  can  be  too  careful. 
The  problem  is  so  simple  that  any  student  who  wishes  to 
succeed  should  have  no  difliculty.  He  may  be  sure 
that  he  will  never  learn  to  draw  until  he  is  able  to  dis- 
cover his  mistakes,  and  as  the  use  of  the  thread  is  a 
most  important  test,  it  should  be  correctly  aj)plied. 

Any  object,  as  the  cube,  Fig.  14,  having  been  drawn, 
it  may  be  tested  by  the  thread  as  follows  :  Hold  the 
thread  horizontal  to  cover  point  5,  and  note  its  apparent 
intersections  with  the  edges  1-6  and  6-7.  Hold  the 
thread  vertical  in  front  of  point  3,  and  see  where  it 
intersects  5-6.  Hold  it  in  front  of  6-7,  and  notice  its 
intersection  with  2-3.  Hold  the  thread  to  cover  i  and 
5,  also  2  and  4,  and  compare  the  directions  with  a  hori- 
zontal line.     Continue  the  edge  2-7  to  intersect  5-6,  and 


TESTS. 


4-7  to  intersect  2-1.     Cover  any  opposite  points  as   i 
and   3,   3   and  6,  4   and   r,  etc.,  and  notice  where  the 


1  !irpnii_ai\ru»arc  tr\ 

T/Q.  ^  /^  _ 


"edges  between, 
ply  a  more  exact  method 
wing  lines  in  the  air,  the 

1  the  eye  is  trained,  the 
ipler,  is  all  that  is  needed. 

2  use  of  the  thread  pref- 
which  can  be  made  to 
object,  and  its  intersec- 
miich  more  readily  than 

1  or  nile,  which  hides  con- 
■se  tests  with  the  threarl 
)  discover  every  error  of 


(T.)  A  last  test  may  be  applied  by  holding  two  pencils 
together  at  right  angles  to  the  direction  in  which  the 
object  is  seen,  and  separating  them  until  one  covers  2-3 
and  the  other  covers  5-6.  If  great  care  is  taken,  the 
directions  of  these  lines  with  reference  to  each  other  may 
be  seen,  and  the  drawing  tested  by  continuing  these  lines 
in  the  drawing. 

(1\)  One  way  of  measuring  the  apjiarent  angle  between 
lines  is  by  folding  a  piece  of  paper  and  holding  it  so  that 
each  part  appears  to  coincide  with  one  of  the  two  lines. 
This  way  is  easiest  applied  by  the  use  of  a  hinged  rule 
or  straight    edge  of  two    parts.     I    cannot    recommend 


74  FKEE-iiAND  DRAWING. 

ture  ("  not  foreshortened  "),  they  will  appear  horizontal 
and  will  jjlace  the  thread  correctly ;  but  if  the  horizontal 
lines  of  the  subject  are  not  thus  situated,  they  will  not 
appear  horizontal,  and  so  will  ca'"-"  **■•-  ♦'-       ' 
of  level. 

It  may  seem  that  unnecessary  j 
thes^  directions,  but  it  has  been  f 
to  make  many  students  understan 
the   thread  correctly,   even  after 
and    illustrations.      Some,   after 
found  holding  the  thread  or  j)enci 
ten  to  thirty  degrees  away  from  th< 
it  is  thought  that  no  explanatioi 
The  problem  is  so  simple  that  any 
succeed   should  have  no  difficult) 

that  he  will  never  learn  to  draw  u .o  auic  lo  ais- 

cover  his  mistakes,  and  as  the  use  of  the   thread  is  a 
most  important  test,  it  should  be  correctly  applied. 

Any  object,  as  the  cube.  Fig.  14,  having  been  drawn, 
it  may  be  tested  by  the  thread  as  follows  :  Holil  the  / 
thread  horizontal  to  cover  point  5,  and  note  its  apparent 
intersections  with  the  edges  1-6  and  6-7.  Hold  the 
thread  vertical  in  front  of  point  3,  and  see  where  it 
intersects  5-6.  Hold  it  in  front  of  6-7,  and  notice  its 
intersection  with  2-3.  Hold  the  thread  to  cover  i  and 
5,  also  2  and  4,  and  compare  the  directions  with  a  hori- 
zontal line.     Continue  the  edge  2-7  to  intersect  5-6,  and 


TESTS.  75 

4-7  to  intersect  2-1.  Cover  any  opposite  points  as  i 
and  3,  3  and  6,  4  and  i,  etc.,  and  notice  where  the 
thread  appears  to  intersect  the  edges  between. 

This  use  of  the  thread  is  simply  a  more  exact  method 
of  discovering  angles  than  drawing  lines  in  the  air,  the 
first  method  explained.  AVhen  the  eye  is  trained,  the 
first,  which  is  of  course  the  simpler,  is  all  that  is  needed. 
But  most  students  will  find  the  use  of  the  thread  pref- 
erable, as  it  gives  a  fine  line  which  can  be  made  to 
exactly  cover  the  edges  of  the  object,  and  its  intersec- 
tion with  the  edges  can  be  seen  much  more  readily  than 
that  of  a  line  formed  by  a  pencil  or  rule,  which  hides  con- 
siderable of  the  object.  If  these  tests  with  the  thread 
are  applied,  they  cannot  fail  to  discover  every  error  of 
importance. 

(T.)  A  last  test  may  be  applied  by  holiling  two  pencils 
together  at  right  angles  to  the  direction  in  which  the 
object  is  seen,  and  separating  them  until  one  covers  2-3 
and  the  other  covers  5-6.  If  great  care  is  taken,  the 
directions  of  these  lines  with  reference  to  each  other  may 
be  seen,  and  the  drawing  tested  by  continuing  these  lines 
in  the  drawing. 

(T.)  One  way  of  measuring  the  apparent  angle  betwee?! 
lines  is  by  folding  a  piece  of  paper  and  holding  it  so  that 
each  part  appears  to  coincide  with  one  of  the  two  lines. 
This  way  is  easiest  applied  by  the  use  of  a  hinged  rule 
or  straight    edge  of  two    parts.     I    cannot    recommend 


76  FREE-HAND  DRAWING. 

this  test,  for  there  are  two  straight  edges  to  be  held  at 
right  angles  to  the  direction  in  which  the  student  looks, 
and  it  is  so  difficult  to  do  this  that  I  do  not  know  of 
many  students  who  have  succeeded.  Those  who  can  hold 
the  rules  correctly,  may  depend  upon  their  eyes  and  get 
the  drawing  better  without  many  mechanical  tests  than 
with  them. 

(T.)  Another  way  of  testing  the  direction  of  a  long 
line  is  to  hold  a  straight  edge  upon  the  line  of  the  draw- 
ing, and  then  lift  the  board  and  straight  edge  into  the 
position  of  the  picture  plane,  when  the  straight  edge 
appears  to  coincide  with  the  line  if  its  direction  in  the 
drawing  is  correct. 

I  have  dwelt  thus  carefully  upon  each  test  in  tlie 
hope  that  the  student  may  realize  their  importance,  for 
he  will  learn  to  draw  correctly  only  through  his  own 
efforts,  gaining  with  each  discovery  of  error.  He  can 
never  become  a  draughtsman  as  long  as  he  depends  upon 
a  teacher  for  corrections.  Let  him  carry  his  drawing  so 
far  that  a  thorough  application  of  the  tests  explained 
will  show  no  error,  then  as  it  is  simply  a  question  of 
exactness  to  be  determined  by  the  eye,  if  the  trained  eye 
of  the  teacher  discovers  mistakes  so  slight  that  the  stu- 
dent cannot  rightly  be  expected  to  determine  them,  these 
may  be  pointed  out.  As  the  chief  benefit  resiilts  from 
what  the  student  himself  sees  and  does,  he  will  be  much 
better  off  without  a  teacher  than  with  one  who  does  his 
work  for  him. 


TESTS.  77 

As  stated  on  page  23,  the  art  student  should  use  few 
texts  and  should  not  require  the  mechanical  aids  to  test- 
ing which  have  been  explained.  They  may  sometimes 
be  required  by  teachers  in  the  public  schools,  when 
students  have  no  capacity  for  the  work,  but  even  then 
they  will  not  be  necessary  if  the  glass  is  used  to  train 
the  eye  to  see  proportions,  or  as  a  means  for  testing.  In 
all  work,  the  student  should  aim  to  use  few  aids  and  to 
throw  these  aside  as  soon  as  possible. 

There  are  many  who  say  that  measurements  and  tests 
are  mechanical,  and  that  to  learn  to  draw  the  student 
should  draw  by  eye  simply.  It  is  true  that  measurements 
and  tests,  as  unfortunately  too  many  students  are  taught 
to  use  them,  cannot  fail  to  produce  hard  and  mechanical 
drawings  and  retard  progress.  Still  it  seems  better  for 
the  student,  when  he  can  see  no  farther,  to  be  shown  by 
tests  where  his  eyes  have  failed,  rather  than  to  carry  draw- 
ings only  as  far  as  he  can  by  eye,  and  then  put  them  away 
and  begin  others  which  can  be  carried  but  Httle  if  any 
f^irther.  Therefore  the  student  is  advised  to  apply  the 
tests  explained  after  he  has  carried  his  drawings  as  for  as 
he  can  see,  and  not  to  put  any  drawings  away  which  the 
tests  show  to  be  untruthful.  It  is  believed  that  thi?  train- 
ing will  most  quickly  produce  ability  to  draw  truthfully  at 
sight. 


CHAPTER   VI. 
Perspective  Principles. 

(See  Preface,  page  vii.) 

"  Our  whole  past,  and  especially  the  ideas  and  emo- 
tions of  the  present  moment,  determine  how  we  perceive 
any  object." 

This  being  true,  the  student  must  work  long  and 
earnestly  before  he  can  separate  facts  from  appearances, 
as  the  knowledge  of  the  actual  form  prevents  the  mind 
from  accepting  its  appearance.  The  impression  con- 
veyed to  the  mind  of  one  not  trained  to  accept  the  image 
of  the  eye,  is  the  result  of  a  combination  of  what  the  eye- 
sees  with  what  is  by  far  the  greatest  factor,  what  the  mind 
knows  concerning  the  actual  conditions  of  the  object. 
The  student  must  struggle  continually  not  only  against 
this  influence  of  his  mind,  but  also  against  the  effect 
which  one  line  exerts  to  change  the  apparent  directions 
of  otl»ers.  This  effect  is  sometimes  so  strong  that  even 
the  practised  eye  of  the  artist  is  deceived,  and  we  may 
safely  say  that  the  most  perfect  eye,  with  the  longest 
training,  is  liable  to  be  deceived.  A  knowledge  of  the 
perspective  principles  governing  the  appearance  of  form 
78 


PERSPECTIVE  PRINCIPLES.  79 

is  tlnis  helpful  to  the  draughtsman  who  would  be  truthful, 
and  there  is  no  reason  why  there  should  not  be  truth  and 
artistic  renderins;  at  the  same  time. 


Tlie  Plane  of  the  Drawing. 

The  mind  through  the  sense  of  sight  perceives  form, 
the  rays  of  light  from  any  object  entering  the  eye,  being 
focused  on  the  retina,  and  forming  an  image  of  the  object, 
as  in  the  camera,  except  that  in  the  latter  the  image  is 
formed  on  a  plane  surface,  while  that  in  the  eye  is  formed 
on  a  spherical  surface.  As  but  a  single  point  can  be  seen 
clearly  at  any  time,  the  image  of  the  eye  is  practically 
the  same  as  that  of  the  camera. 

The  artist's  problem  is  to  make  his  drawing  so  that  it 
shall  create  the  same  ideas  of  form,  size,  and  position  as 
the  objects  which  it  represents.  It  is  evident  that  this 
must  occur  when  the  drawing  produces  the  same  image 
in  the  eye  as  the  objects.  To  do  this  the  drawing  must 
be  similar  to  the  image. 

The  rays  from  any  object  to  the  eye  form  a  conical 
body.  If  this  cone  of  rays  is  intersected  by  any  plane,  the 
intersection  is  a  picture  of  the  object,  which  if  the  object 
is  taken  away,  will  still  create  its  image  in  the  eye.  If 
this  plane  of  the  picture  is  at  right  angles  to  the  cone,  the 
section  (the  picture)  will  be  a  true  picture  of  the  object, 
that  is,  be  similar  to  the  image  of  the  eye. 


so  FREE-HAND   DRAWING. 

Figure  15  represents  a  circle  A,  placed  vertical  and  in 
front  of  the  eye.  The  cone  formed  by  the  visual  rays  is 
represented  by  lines  h-b,  and  a  vertical  plane  cutting 
through  the  cone  of  rays,  by  line  P.  If  the  student  will 
hold  any  cone  horizontal,  it  will  perfectly  illustrate  the 
figure,  the  base  of  the  cone  representing  the  circle  A,  and 
the  apex  representing  the  eye.  With  the  cone  the 
student  will  at  once  see  that  a  vertical  plane  between 
the  eye  and  the  base  intersects  the  cone  in  a  circle.  This 
circle  is  the  picture  of  the  base  A. 

Figure  16.  If  now  the  plane  of  the  picture  is  inclined 
to  the  axis  of  the  cone,  its  intersection  with  the  cone  is 
still  a  picture  of  the  circle,  but  in  shape  it  differs  from 
that  in  Fig.  15,  which  is  a  circle.  The  oblique  intersec- 
tion is  an  ellipse,  but  it  is  important  to  notice  that  it  docs 
not  appear  such  to  the  eye  at  the  apex  of  the  cone.  It 
appears  a  circle  exactly  covering  the  base  of  the  cone. 
It  makes  no  difference  how  the  plane  of  the  picture  is 
placed,  or  what  the  proportions  of  the  resulting  ellipse, 
it  must  always  appear  to  the  eye  a  circle,  in  fact,  the 
circle  of  the  base.  When  the  eye  is  removed  from  the 
apex  of  the  cone,  the  ellipse  appears  an  ellipse,  and  is  not  a 
true  picture  of  the  circle.  The  circle  of  Fig.  15  and  the 
ellipse  of  Fig.  16  are  pictures  of  the  circle  A,  and  create 
in  the  eye,  when  it  is  at  the  apex,  a  circular  image  of  the 
circle,  but  the  former  only  is  similar  to  the  object  A. 
When  looking  at  pictures  we  naturally  hold  them  in 


This  must  be  at  rignt  angles  lu  mc  xmw^i.v^..  .., _  . 

the  object  is  seen.     The  plane  cannot  be  perpendicular 
lo  all  the  rays,  but  should  be  so  to  the  central  one.    ih-f  ^*> 

A  "  tnie  "  picture  of  any  object  may  be  obtained  by 
drawing  upon  a  sheet  of  glass  with  a  brush  and  color,  or 
a  special  pencil,  or  on  a  wire  screen  with  chalk.  The 
gKiss  or  screen  should  be  placed  at  right  angles  to  a  line 
from  the  centre  of  the  object  to  the  eye,  the  eye  and 
screen  held  in  one  position,  and  lines  drawn  to  cover  all 
tiie  edges  which  are  seen.  It  is  desired  that  every  stu- 
dent make  drawings  in  this  way,  a  small  pane  of  glass  and 
a  special  pencil  being  the  best  materials.  The  drawings 
should  be  made  with  the  glass  at  right  angles  to  the  rays, 
also  when  it  is  held  obliiiuely.      The  drawings  may  be 


X 


tion  is  an  ellipse,  but  it  is  important  to  notice  that  it  does 
not  appear  such  to  the  eye  at  the  apex  of  the  cone.  It 
appears  a  circle  exactly  covering  the  base  of  the  cone. 
It  makes  no  difference  how  the  plane  of  the  picture  is 
placed,  or  what  the  proportions  of  the  resulting  ellipse, 
it  must  always  appear  to  the  eye  a  circle,  in  fact,  the 
circle  of  the  base.  When  the  eye  is  removed  from  the 
apex  of  the  cone,  the  ellipse  appears  an  ellipse,  and  is  not  a 
true  picture  of  the  circle.  The  circle  of  Fig.  15  and  the 
ellipse  of  Fig.  16  are  pictures  of  the  circle  A,  and  create 
in  the  eye,  when  it  is  at  the  apex,  a  circular  image  of  the 
circle,  but  the  former  only  is  similar  to  the  object  A. 
When  looking  at  pictures  we  naturally  hold  them  in 


PERSPECTIVE  PRINCIPLES.  81 

front  of  us,  at  right  angles  to  our  line  of  vision,  as  in  the 
position  of  the  plane  P  of  Fig.  15.  If  plane  P  of  Fig.  16 
is  thus  held,  the  ellipse  upon  it  appears  an  ellipse,  and 
cannot  create  the  idea  of  a  circle.  We  see  that  the  first 
picture  is  preferable  to  the  second,  for  it  is  a  circle,  and 
wherever  the  eye  is  placed  creates  a  circle  in  the  eye. 
(It  is  of  course  understood  that  it  is  always  looked  at 
jierpendicularly. ) 

We  will  distinguish  the  first  picture  from  that  given  by 
any  other  position  of  the  picture  plane,  by  calling  it  a 
tme  picture^  meaning  that  it  is  similar  to  the  image 
created  in  the  eye  by  the  object.  There  can  be  but  one 
jiosition  of  the  picture  plane  which  giv^es  a  "  true  "  picture. 
This  must  be  at  right  angles  to  the  direction  in  which 
the  object  is  seen.  The  plane  cannot  be  perj')endicular 
to  all  the  rays,  but  should  be  so  to  the  central  one.    t*-/  '** 

A  "  true  "  picture  of  any  object  may  be  obtained  by 
drawing  upon  a  sheet  of  glass  with  a  brush  and  color,  or 
a  special  pencil,  or  on  a  wire  screen  with  chalk.  The 
gliss  or  screen  should  be  placed  at  right  angles  to  a  line 
from  the  centre  of  the  object  to  the  eye,  the  eye  and 
screen  held  in  one  position,  and  lines  drawn  to  cover  all 
the  edges  which  are  seen.  It  is  desired  that  every  stu- 
tient  make  drawings  in  this  way,  a  small  pane  of  glass  and 
a  special  pencil  being  the  best  materials.  The  drawings 
should  be  made  with  the  glass  at  right  angles  to  the  rays, 
also  when  it  is  held  obli<|uely.      The  drawings  may  be 


82 


FREE-IUA'D  DRA  WING. 


compared,  and  the  student  realize  that  the  glass  must 
be  perpendicular  to  the  direction  in  which  he  looks  for 
the  drawing  to  give  the  real  appearance  of  the  object. 

It  appears  that  a  drawing  on  any  plane  or  surface 
creates  the  correct  impression,  only  when  the  eye  is  in 
the  position  which  it  had  when  the  drawing  was  made. 
All  drawings,  then,  are  best  seen  from  some  one  point  or 
distance.  The  trained  eye  will  select  this  distance.  As, 
however,  drawings  and  pictures  will  be  viewed  by  un- 
trained eyes,  and  as  the  proper  point  may  not  always  be 
accessible,  it  is  important  that  all  should  be  avoided 
which  causes  marked  distortion,  when  the  picture  is  not 
seen  from  the  proper  point.  If  the  picture  is  a  "true" 
picture,  the  distortion  produced  when  it  is  viewed  from 
too  long  or  short  a  distance,  appears  not  in  the  shape  of 
its  parts,  but  only  in  the  relative  sizes  of  the  objects 
represented.  Thus  the  distortion  of  a  "  true  "  picture  is 
always  less  than  that  of  a  drawing  on  a  plane  oblique  to 
the  visual  rays,  and  the  "  tnie  "  jiicture  is  by  f:ir  the  best 
drawing  th.it  can  be  made  for  general  use.  It  is  called 
a  Model  Drawing. 

Before  beginning  the  problems,  we  will  choose  a  term 
which  shall  mean  the  position  in  which  any  line  appears 
its  real  length,  and  any  plane  its  real  shape.  This 
occurs  when  the  line  or  the  plane  is  perpendicular  to  the 
direction  in  which  it  is  seen,  that  is,  is  parallel  to  the 
picture  plane.     The  words  "  parallel  to  the  picture  plane  " 


PERSPECTIVE  PRINCIPLES.  83 

might  cause  confusion,  from  the  fact  that  in  perspective 
the  picture  plane  is  generally  vertical,  and  takes  in  a 
wide  field  of  view,  while  in  Model  Drawing  the  plane  is 
perpendicular  to  the  direction  in  which  one  looks,  and  is 
thus  continually  changing.  We  wish  a  term  which  shall 
mean  the  position  in  which  any  line  appears  its  real 
length  and  any  jjlane  its  real  shape,  and  will  select  the 
words  not  foreshortened.  Any  line  is  "  not  foreshort- 
ened  "  when  its  ends  are  etjually  distant  from  the  eye, 
ami  any  plane  when  its  angles  are  equally  distant. 

^\'e  must  also  decide  upon  a  term  which  shall  mean 
the  appearance  of  the  facts  instead  of  the  facts.  We 
select  pcrspcctively.  "  Perspectively  "  parallel  thus  means 
the  appearance  of  parallel  lines,  which  is  that  of  conver- 
gence. "  Perspectively "  parallel  lines  are  lines  which 
converge    towards    a  point,  and    "perspectively"  equal  p 

distances  on  any  line  are  unequal,  the  space  representing 
the  nearest  of  the  equal  distances  being  the  longest,  as  in 
Fig.  24.  X    f.fO 

The  apparent  angle  at  which  parallel  lines  seem  to 
converge,  that  is,  the  angle  between  the  lines  represent- 
ing i^arallel  lines,  we  may  speak  of  as  large  or  small,  and 
say  that  lines  converge  or  vanish  quickly  or  slowly. 
They  vanish  quickly  when  the  vanishing-point  is  near  the 
drawing,  and  slowly  when  it  is  far  from  the  drawing. 

The  angle  which  any  line  appears  to  make  with  a 
horizontal  line  that  appears  horizontal,  we  will  call  the 

A-    ^     y^^,^^^/.  e  3.  ^.67 


K" 


i'...,!; 


Jil 


r/a.ir 


X3--^ 


84 


FREE-HAND  DRA  WING. 


angle  of  inclination.  Thus  all  horizontal  lines  whose  ends 
are  not  e(iui-clistant,  appear  to  incline  at  smaller  or 
greater  "  angles  of  inclination,"  according  to  the  anglei: 
which  the  lines  make  with  the  picture  plane.  Lines  not 
level  appear  inclined  at  "  angles  of  inclination  "  which 
increase  with  the  angles  of  the  lines  with  the  picture 
plane  and  the  ground.  The  "  angles  of  inclination  "  of 
liorizoutal  lines  increase  or  decrease  with  the  distance  of 
the  vanishing-point,  that  is,  with  the  angle  of  convergence. 
In  all  the  problems  explained,  the  picture  plane  is 
supposed  to  touch  the  object  at  its  nearest  point,  and 
the  drawing  is  the  largest  possible  to  be  made  on  a  plane 
in  front  of  the  object. 


i/zi 


^  1%  f 


Study  of  Principles. 

Figure  1 7.  Place  a  large  cube  a  few  feet  distant  from 
the  eye,  so  that  its  centre  is  on  the  level  of  the  eye, 
four  of  its  edges  vertical,  and  one  face  visible,  with  its 
angles  equally  distant  from  the  eye.  This  face  is  "  not 
foreshortened,"  and  appears  its  real  shape. 

Figure  18.  Turn  the  cube  so  that  its  left  side  appears 
very  narrow.  It  will  be  noticed  that  the  upper  end  of 
the  farther  vertical  edge  B  appears  below  the  upper  end 
of  the  front  edge  A,  and  that  the  lower  end.  of  the 
farther  edge  appears  above  the  lower  end  of  the  front 
edge.     The  farther  edge  thus  appears  shorter  than  the 


PERSPECTIVE   PREXCIPLES. 


85 


front  edge.  It  is  also  seen  that  the  horizontal  edges  D 
and  E,  whicli  connect  the  ends  of  these  verticals,  appear 
to  converge.  If  these  lines  of  the  drawing  are  con- 
tinued, they  will  meet.  The  continued  lines  must  be  the 
representations  of  continuations  of  the  edges,  and  we  see 
that  parallel  retreating  lines  in  Nature  appear  to  con- 
verge to  a  point  called  their  vanishing-point.      1^/- 

We  now  find  that  the  right  Q(\^<i.  C  is  farther  from  the 
eye,  and  thus  appears  shorter  than  the  central  edge  A, 
and  the  horizontal  edges  F  and  G  appear  to  converge,  as 
the  horizontal  edges  of  the  left  face.  The  edge  C  is 
much  nearer  the  eye  than  B,  and  appears  longer.  It  is 
really  but  little  farther  from  the  eye  than  A,  and  the  con- 
vergence of  F  and  G  is  very  slight.  As  the  eye  is 
oi)posite  the  centre  of  the  cube,  the  apparent  distances 
that  the  upper  ends  of  B  and  C  are  below  that  .of  A 
must  be  the  same  as  the  apparent  distances  of  the  lower 
ends  of  B  and  C  above  that  of  A;  arid  the  "angles  of 
inclination "  of  the  upper  edges  D  and  G  must  be  the 
same  as  those  of  the  lower  edges  E  and  F.  Since  these 
edges  appear  equally  inclined,  they  will  appear  to  vanish 
on  the  level  Q^Jhe  centre  of  the  cube,  that  is,  of  the  eye. 

If  now  the  eye  is  lifted,  the  '*  angles  of  inclination  " 
at  the  top  decrease,  and  those  at  the  bottom  increase. 
When  the  eye  comes  to  the  level  of  the  top  of  the  cube, 
the  upper  angles  disappear,  and  the  whole  top  is  seen  as 
a  horizontal  line. 

^         CL 


"fj/S 


^j.fi<- 


io 


S6  J-REE-J/AA'D  DRAWING. 

From  this  study  of  the  cube,  we  see, — 

I  St.  That  of  two  i)arallel  and  equal  Hnes  which  do  not 
vanish,  the  nearer  appears  the  longer.  The  relative 
lengths  appear  to  decrease  as  the  distances  increase. 
See  Fig.  19,  in  which  B  being  twice  the  distance  of  A 
from  the  eye,  appears  one-half  as  long  as  A. 

2d.  That  parallel,  retreating  lines  appear  to  converge 
towards  a  point,  called  their  vanishing-point.  (All  lines 
whose  ends  are  unequally  distant  from  the  eye  are 
retreating  lines.) 

3d.  That  horizontal,  retreating  lines  appear  to  de- 
scend or  vanish  downward  when  the  lines  are  above  the 
level  of  the  eye,  and  to  ascend  or  vanish  ujiward  when 
they  are  below  the  level  of  the  eye.  This  is  evident  from 
the  fact  that  the  eye  must  be  dropped  to  look  from  the 
nearer  to  the  farther  end  of  the  line  above  the  eye,  and 
be  raised  to  look  from  the  nearer  end  of  the  line  below 
the  eye  to  its  farther  end. 

4th.  That  i)arallel,  retreating  horizontal  lines  appear 
to  vanish  at  the  level  of  the  eye. 

5th.  That  a  horizontal  line  at  the  level  of  the  eye 
appears  horizontal,  and  a  horizontal  plaice  at  this  level 
is  seen  edgewise,  and  appears  a  horizontal  line. 

We  will  now  draw  upon  the  wall  of  any  room   lines 

which'  have  the    apparent   directions    of  the    horizontal 

lines  A,  B,  C  and  D,  at  floor  and  ceiling,  which  are  per- 

— ' A 

pendicular  to  the  wall.     We  find  that  the  lines  on  the 


J^<^  ^  ^^ 


S7 

he  eye.  Par- 
oint  infinitely 
e  transparent, 

continue  on 
to    converge. 

the  continu- 
se  lines,  (the 

]3oint  in  the 
.  This  2gint 
room  passing 
:)Ugh  the  eye 

/  litics  is  in  a 


To  draw  the  lines  on  the  side  of  a  room,  two  students 
must  work  together,  one  observing,  the  other  drawing  the 
lines  with  a  straight  edge.  But  the  students  may  work 
individually  by  drawing  a  sketch  of  any  room,  the  direc- 
tions of  the  perpendiculars  to  the  end  being  determined 
by  holding  the  thread  or  a  ruler  to  cover  the  lines.  This 
experiment  proves  that  to  see  tlie  vanishing-point  of  a  sys- 
tem of  parallel  lines,  we  must  look  in  their  direetion. 

All  parallel  lines  luhich  have  one  end  nearer  the  eye 
than  the  other  appear  to  converge,  and  the  convergence  is 
in  the  direction  of  their  farther  ends.  According  to  this 
statement,  the  vertical  edges  of  a  cube  above  or  below  the 
eye  appear  to  converge,  but  they  are  not  so  represented.   In 


^(Uiu^^i^ 


%rT 


ao 


S6  FKEE-ll 

From  this  study  of  th 

I  St.  That  of  two  parai 
vanish,  the  nearer  app( 
lengths  appear  to  decn 
See  Fig.  19,  in  which  B 
from  the  eye,  appears  om 

2d.  That  iiarallel,  retr 
towards  a  point,  called  th 
whose  ends  are  unequa 
retreating  lines.) 

3d.  That  horizontal,  n 
scend  or  Vanish  downward 
level  of  the  eye,  and  to  a 
they  are  below  the  level  of 

the  fact  that  the  eye  must  ^  ^        ._  .o^n.  11  om  the 

nearer  to  the  farther  end  of  the  line  above  the  eye,  and 
be  raised  to  look  from  the  nearer  end  of  the  line  below 
the  eye  to  its  farther  end. 

4th.  That  parallel,  retreating  horizontal  lines  ap[>ear 
to  vanish  at  the  level  of  the  eye. 

5th.  That  a  horizontal  line  at  the  level  of  the  eye 
appears  horizontal,  and  a  horizontal  plaiie  at  this  level 
is  seen  edgewise,  and  appears  a  horizontal  line. 

We  will  now  draw  upon  the  wall  of  any  room  lines 
which'  have  the   apparent   directions    of  the    horizontal 

lines  A,  B,  C  and  D.  at  floor  and  ceiling,  which  are  per- 

— — — A 

pendicular  to  the  wall.     We  find  that  the  lines  on  the 


PERSPECTIVE  PRTNCrPLES.  87 

wall  intersect  at  a  point  directly  opposite  the  eye.  Par- 
allel  lines  in  Nature  appear  to  meet  at  a  point  infinitely 
distant.  Suppose  the  end  of  the  room  to  be  transparent, 
and  the  lines  perjjendicular  to  the  end  to  continue  on 
the  other  side.  Retreating,  they  appear  to  converge. 
The  lines  drawn  on  the  end  are  pictures  of  the  continu- 
ing lines.  The  point  on  the  wall  where  these  lines,  (the 
j)ictures,)  meet  must  be  the  picture  of  the  point  in  the 
infinite  distance  where  the  actual  lines  meet.  This  point 
is  in  a  perpendicular  to  the  end  of  the  room  passing 
through  the  eye ;  that  is,  it  is  in  a  line  through  the  eye 
parallel  to  the  lines.     Hence  we  see  that, — 

The  vanishhig-poiiit  of  any  set  of  parallel  lines  is  in  a 
parallel  to  them,  passing  through  the  eye. 

To  draw  the  lines  on  the  side  of  a  room,  two  students 
must  work  together,  one  observing,  the  other  drawing  the 
lines  with  a  straight  edge.  But  the  students  may  work 
individually  by  drawing  a  sketch  of  any  room,  the  direc- 
tions of  the  perpendiculars  to  the  end  being  determined 
by  holding  the  thread  or  a  ruler  to  cover  the  lines.  This 
experiment  proves  that  to  see  the  vanishing-point  of  a  sys- 
tem of  parallel  lines,  we  must  look  in  their  direction. 

All  parallel  lines  which  have  one  etid  nearer  the  eye 
than  the  other  appear  to  converge,  and  the  convergence  is 
in  the  direction  of  their  farther  ends.  According  to  this 
statement,  the  vertical  edges  of  a  cube  above  or  below  the 
eye  appear  to  converge,  but  they  are  not  so  represented.  In 


^(Uic^^^ 


S8 


FREE-HAXD   DRA  WING. 


2 


%■''- 


a  model  drawing  vertical  lines  are  represented  by  verti- 
cal lines  (see  page  96). 

Figure  21.  Place  a  cube  so  that  its  top  and  front  faces 
are  seen,  and  so  its  right  side  appears  a  vertical  line.  The 
edges  A,  A,  A  have  their  left  ends  a  little  farther  from 
the  eye  than  their  right  ends ;  but  the  distance  is  so 
short  that  the  convergence  is  very  slight,  and  the  edges 
appear  practically  horizontal.  Line  B  of  the  drawing  is 
longer  than  C,  and  yet  the  edge  C  is  nearer  the  eye  than 
B.  This  proves  inexact  the  statement  frequently  made 
that  "  of  two  parallel  and  equal  hnes,  the  nearer  appears 
the  longer."  ^ 

Figure  22  is  a  top  view,  representing  the  eye,  a  hori- 
zontal square,  and  a  vertical  picture  plane.  It  shows  that 
of  two  parallel  and  equal  lines,  AB  and  CD,  unequally 
distant  from  the  eye,  the  nearer,  AB,  appears  the  shorter 
when  the  lines  are  at  a  greater  angle  than  45°  with  the 
picture  plane.  When  at  a  less  angle  than  45°,  as  Bl) 
and  AC,  the  nearer,  BD,  appears  the  longer.  This  state- 
ment is  only  exact  for  lines  whose  angles  are  noticeably 
larger  or  smaller  than  45°. 

The  figure  also  shows  that  of  two  equal  lines,  AB  and 
BO,  i^erpendicular  to  each  other  and  having  one  end 
common,  the  one  which  makes  the  greater  angle  in'ith  the 
picture  appears  the  shorter  ;  or  conversely,  the  one  nearest 
parallel  appears  the  longer.  It, shows,  too,  that  if  one 
line  of  a  right  angle  z'anishes  toward  the  left,  the  other 
must  vanish  toward  the  right. 


T^ 


PERSPECTIVE  PRINCIPLES. 


89 


If  one  side  of  the  right  angle  is  "  not  foreshortened," 
the  other  side  extends  directly  away  from  the  spectator, 
and  vanishes  at  a  point  above  the  side  "  not  fore- 
shortened," on  the  level  of  the  eye. 

Figure  23  shows  that  two  equal,  horizontal  lines,  per- 
Ijendicular  to  each  other,  at  equal  angles  with  the  picture, 
appear  equal  in  length.  When  below  or  above  the  level 
of  the  eye  they  are  at  equal  "  angles  of  inclination." 

In  Figs.  22  and  23,  the  visual  rays  intersect  the  pic- 
ture plane,  and  give  the  positions  upon  the  picture  plane 
of  the  vertical  lines  which  contain  the  ends  of  the  lines 
representing   the    sides   of  the  square,  which   are  thus 


i2i       l%i^ 


S8 


FREE-HAND   DRAWING. 


a  model  drawing  vertical  lines  are  represented  by  verti- 
cal lines  (see  page  96). 

Figure  21.  Place  a  cube  so  that  its  top  and  front  faces 
are  seen,  and  so  its  right  side  appears  a  vertical  line.  The 
edges  A,  A,  A  have  their  left  ends  a  little  farther  from 
the  eye  than  their  right  ends ;  but  the  distance  is  so 
short  that  the  convergence  is  very  slight,  and  the  edges 
appear  practically  horizontal.  Line  B  of  the  drawing  is 
longer  than  C,  and  yet  the  edge  C  is  nearer  the  eye  than 
B.  This  proves  inexact  the  statement  frequently  made 
that  "  of  two  parallel  and  equal  lines,  the  nearer  ajjpears 
the  jQn£er.!li^ __^ 

] 
zor 
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dis 
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pic 
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me 
lar 


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BI 

CO 

pic 

p:i 

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PERSPECTIVE  PKIXCIPLES.  89 

If  one  side  of  the  right  angle  is  "  not  foreshortened," 
the  other  side  extends  directly  away  from  the  spectator, 
and  vanishes  at  a  point  above  the  side  "not  fore- 
shortened," on  the  level  of  the  eye. 

Figure  23  shows  that  two  equal,  horizontal  lines,  per- 
jiendicular  to  each  other,  at  equal  angles  with  the  picture, 
appear  equal  in  length.  When  below  or  above  the  level 
of  the  eye  they  are  at  equal  "  angles  of  incHnation." 

In  Figs.  22  and  23,  tlie  visual  rays  intersect  the  pic- 
ture plane,  and  give  the  positions  upon  the  picture  plane 
of  the  vertical  lines  which  contain  the  ends  of  the  lines 
representing  the  sides  of  the  square,  which  are  thus 
longer  than  the  distances  seen  in  the  plan. 

The  apparent  length  and  angle  of  any  retreating  line 
depends  upon  its  angle  with  the  picture,  the  level  of  the 
line,  (referred  to  the  eye),  and  the  distance  of  the  eye 
from  the  line. 

The  greater  the  angle  of  any  line  with  the  picture,  the 
more  it  is  foreshortened,  and  the  greater  the  "  angle  of 
inclination." 

As  the  eye  is  lifted,  the  "  angles  of  inclination  "  of  the 
lines  AB  and  CD,  Figs.  22  and  23,  increase.  Placing 
the  eye  nearer  the  lines  produces  the  same  effect,  but 
the  "  angles  of  inclination  "  must  always  be  much  less 
than  the  real  angles  which  the  hnes  make  with  the  pic- 
ture plane.  The  "  angle  of  inclination  "  decreases  as 
tlie  eye  apj>roaches  the  level  of  the  line,  and  also  as  the 
distance  of  the  eye  increases. 


90  FKEE-JIAND  DRAWIMG. 

The  statement  often  made  that  "of  parallel  and  equal 
lines  the  more  distant  appears  the  shorter,"  has  prob- 
ably accomplished  as  much  harm  as  good,  for  it  is  only 
true  of  lines  "  not  foreshortened,"  and  of  vertical  lines 
within  the  limits  of  ordinary  drawings.  It  is  not  neces- 
sary to  think  of  this  point  in  the  case  of  horizontal  lines, 
for  therq  are  other  tests  upon  which  it  is  always  better  to 
depend. 

Figure  24.  AB  represents  a  horizontal  line  lying  upon 
the  ground,  and  i,  2,  3,  etc.,  equi-distant  points  in  the  line. 
The  lines  from  these  points  to  tlie  eye  represent  the 
visual  rays  by  which  the  points  are  seen.  These  rays, 
intersecting  the  picture  plane,  show  that  the  equal  dis- 
tances appear  unequal,  the  nearest  appearing  the  longest, 
and  the  farthest  the  shortest,  the  apparent  kngth  decreas- 
ing as  the  distance  increases.  This  is  always  true  of  the 
appearance  of  equal  lengths  on  retreating  lines. 

There  are  three  sets  of  parallel  lines  in  the  cube. 
l2  *  ^    tUl*'  They  all  appear  to  vanish  unless  they  are  "not   fore- 

shortened," and  are  so  rejiresented  except  when  they  are 
vertical,  or  are  situated  as  in  Figs.  21  and  25. 

They  vanish  in  the  directions  of  their  farther  ends, 
and  these  are  points  of  the  invisible  faces  of  the  object. 

If  both  ends  of  an  edge  are  points  of  an  invisible  side 
of  the  object,  the  edge  must  be  considered  as  "  not 
foreshortened,"  even  when  the  eye  is  not  opposite  its 
centre. 


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Figure  24.  AB  represents  a  horizontal  line  lying  upon 
the  ground,  and  i,  2,  3,  etc.,  equi-distant  points  in  the  line. 
The  lines  from  these  points  to  the  eye  represent  the 
visual  rays  by  which  the  points  are  seen.  These  rays, 
intersecting  the  picture  plane,  show  that  //if  equal  dis- 
tances appear  unequal,  the  nearest  appearing  the  longest, 
and  the  farthest  the  shortest,  the  apparent  length  decreas- 
ing as  the  distance  increases.  This  is  always  true  of  the 
appearance  of  equal  lengths  on  retreating  lines. 

There  are  three  sets  of  parallel  lines  in  the  cube. 
They  all  appear  to  vanish  unless  they  are  "  not  fore- 
shortened," and  are  so  represented  except  when  they  are 
vertical,  or  are  situated  as  in  Figs.  21  and  25. 

They  vanish  in  the  directions  of  their  farther  ends, 
and  these  are  points  of  the  invisible  faces  of  the  object. 

If  both  ends  of  an  edge  are  points  of  an  invisible  side 
of  the  object,  the  edge  must  be  considered  as  "  not 
foreshortened,"  even  when  the  eye  is  not  opposite  its 
centre. 


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^^  .-  A/-^   /»V<jC^    ^2t*^^    Zcn^^^^^^^^    ^^^^^i^*<. 


sf 


PERSPECTIVE  PRINCIPLES.  91 

If  the  eye  is  opposite  one  end,  as  in  Fig.  21,  and  the 
edges  are  short,  they  will  be  best  represented  by  parallel, 
horizontal  lines. 

If  the  edges  aje  long  and  the  eye  is  opposite  or  near 
an  end,  as  in  Fig.  25,  it  may  sometimes  be  better  to 
distort  the  nearer  and  smaller  part  of  the  drawing  in 
flivor  of  the  larger  part,  by  representing  the  lines  as  they 
appear.  This  will  happen  in  an  interior  when  the  prism 
is  at  the  side  of  the  picture  so  that  the  distortion  of  the 
nearer  end  is  not  very  noticeable. 

In  any  drawing  representing  simply  the  prism,  it  will 
generally  be  better  to  give  the  effect  of  a  right  prism, 
and  avoid  the  distortion  of  the  nearer  part  by  making 
the  Hnes  horizontal.  In  general,  parallel  horizontal  lines 
which  extend  on  both  sides  of  the  spectator  should  be 
represented  by  parallel  horizontal  lines.  The  student 
should  not  be  allowed  any  other  way,  but  should  treat 
all  edges  as  "  not  foreshortened,"  when  neither  end  face 
of  the  object  is  visible. 

In  Nature  there  is  no  effect  like  that  given  by  parallel 
perspective.  The  difficulties  which  have  just  been  con- 
sidered are  easiest  settled  by  avoiding  the  question  when 
possible,  by  moving  so  that  an  end  ailpears  and  two  van- 
ishing-points can  be  used,  the  drawing  being  between 
them.  If  one  vanishing-point  is  in  the  drawing,  as  in 
Fig.  9,  the  drawing  must  be  distorted,  for  when  one  line 
of  a  right  angle  vanishes  toward  the  left,  we  expect  to  see 


92  FREE-HAND  DRAWING. 

the  other  vanish  toward  the  right.  When  the  question 
cannot  be  avoided  in  this  way,  and  parallel  straight  lines 
extend  on  both  sides  of  the  spectator,  they  should  be 
represented  by  parallel  straight  lines,  and  in  the  case  of 
horizontal  lines,  by  horizontal  lines. 

Parallel  straight  lines  in  Nature  appear  curved.  This 
is  shown  by  the  shadows  of  clouds  at  sunset,  which  some- 
times may  be  seen  extending  across  the  sky,  converging 
in  the  west  toward  the  sun,  and  in  the  east  toward  a 
point  opposite  the  sun.  Any  straight  lines  which  the 
mind  does  not  know  to  be  straight  will,  if  long,  proiluce 
the  impression  of  curved  lines.  This  is  best  shown  by 
the  rays  of  the  electric  search-light. 

In  many  drawings  from  Nature  by  our  leading  illus- 
trators, the  curvature  resulting  from  drawing  the  differ- 
ent parts  of  long  lines  as  they  appear,  is  very  noticeable. 

Although  the  student  may  have  difficulty  in  seeing  the 
effect  of  curvature,  even  in  long  lines,  he  may  very  easily 
prove  that  curvature  will  result  if  he  draws  the  parts, 
even  of  short  lines,  as  he  sees  them.  This  may  be  done 
by  drawing  from  three  boxes  or  prisms,  placed  a  short 
distance  apart  and  in  a  straight  line,  the  central  box 
being  directly  opposite  him,  so  that  only  two  faces  are 
seen. 

Figiire  26  represents  the  appearance  of  the  left-hand 
box,  lx)th  sets  of  whose  horizontal  edges  appear  to  van- 
ish, for  two  sides  of  the  box  are  seen. 


PERSPECTIVE  PRINCIPLES.  93 

Figure  27  represents  the  central  of  the  three  objects. 
Only  one  set  of  its  horizontal  edges  vanishes,  for  since 
but  one  side  is  seen,  the  other  set  is  "  not  foreshortened." 

Figure  28  represents  the  right-hand  box,  whose  ap- 
pearance must  be  similar  to  that  of  the  box  at  the  left. 

The  vertical  edges  of  the  objects  at  the  sides  are 
farther  from  the  eye  than  those  of  the  central  one,  and 
thus  appear  a  little  shorter  than  the  edges  of  the  latter, 
and  if  the  long  lines  of  the  drawings  are  continued,  they 
will  form  cur\'ed  lines. 

Figures  26,  27,  and  28  are  each  correct  representa- 
tions of  the  appearance  of  a  single  box ;  but  if  they  are 
looked  at  all  at  once  as  a  single  picture,  the  impression 
of  the  objects  being  placed  in  a  curve  is  produced. 
No  one  would  think  of  making  this  drawing  as  a  repre- 
sentation of  three  objects  placed  in  a  straight  line.  The 
drawing  below,  Fig.  29,  would  be  made  by  all,  but  this 
drawing  does  not  represent  correctly  the  appearance  of 
the  boxes  at  either  side,  and  it  appears  that  to  give  the 
correct  general  impression,  drawings  sometimes  cannot 
be  exact  in  detail. 

There  are  some  who  think  that  the  study  of  this  ques- 
tion is  unnecessary,  that  without  theory  all  would  natu- 
rally make  the  drawing,  Fig.  29,  as  a  representation  of  the 
three  boxes.  This  is  probably  true  ;  but  the  knowledge 
that  we  see  as  we  cannot  always  represent  is  very  neces- 
sary, as  is  proved  by  the  many  illustrations  from  the  pens 


/ 


94  FREE-IIAXD  DRAWIXG. 

of  those  who  fail  to  apply  to  a  large  subject  the  reason- 
ing which  gives  Fig.  29,  and  thus  produce  drawings 
which  are  flagrant  violations  of  the  simplest  nile  of  per- 
spective, and  this  is  frequently  the  result  of  the  attempt  to 
draw  by  eye  the  appearance  of  the  parts  of  a  large  sub- 
ject (see  page  49). 

Straight  lines  appear  curved,  but  their  representation 
by  curved  lines  is  generally  unsatisfactory,  and  the  stu- 
dent should  never  be  allowed  to  represent  straight  by 
curved  lines.  As  shown  on  plate  28,  straight  lines  may 
be  substituted  for  tlie  cur\'ed  lines,  changing  the  drawing 
very  little  when  there  are  two  vanishing-j)oints. 

The  influence  of  diagram  perspective,  and  particularly 
the  appearances  of  parallel  perspective,  are  so  powerful, 
that  many  illustrators  do  not  realize  that  they  do  not  see 
parallel  perspectives  in  Nature,  and  that  there  must  l)e 
two  vanishing-points  for  the  horizontal  lines  of  any  rec- 
tangular object,  when  two  of  its  sides  are  seen.  It  is  not 
necessary  to  advise  the  student  not  to  make  as  one  draw- 
ing the  Figs.  26,  27,  and  28,  or  not  to  represent  the  end 
of  a  room  as  curved ;  yet  the  draughtsman  who  would 
never  think  of  making  the  latter  mistake  in  the  case  of  a 
single  unbroken  surface,  will  frequently  do  it  when  the 
surface  is  broken  or  when  there  are  many  short  lines  in 
different  planes. 

Diagram  perspective  has  created  many  false  ideas,  and 
is  responsible  for  much  bad  drawing,  and  yet  the  per- 


HJU 


PERSPECTIVE  PRINCIPLES.  95 

s[)ective  principle  that  straight,  parallel  lines  have  the 
same  vanishing-point  is  absolutely  necessary  to  the  illus- 
trator.* 

Applicatio7t  of  Principles  to  Drmviiigs  of  tlie  Cube. 
A  cube  with  edges  of  four  feet.     Scale  j^  in.  =  i  ft. 

Figure  30.  The  cube  with  four  edges  vertical,  its 
lower  face  on  the  level  of  the  eye,  and  one  surface  visi- 
ble with  its  lower  edge  AB  "  not  foreshortened." 

The  lower  face  appears  a  horizontal  line.  The  upper 
edge  CD  of  the  front  face  is  farther  from  the  eye  than 
AB,  but  unless  the  eye  is  very  near  the  object,  the  face 
will  be  foreshortened  so  little  as  to  appear  practically  its 
real  shape. 

Figure  31.  A  cube  with  its  top^four  feet  below  the  cube 
of  Fig.  30. 

The  receding  horizontal  edges  vanish  at  point  C,  the 
centre  of  edge  AB,  because  this  edge  is  on  the  level  of 
the  ej'.e,  and  a  line  from  its  centre  to  the  eye  is  parallel 
to  the  edges.  The  front  face  is  below  the  eye,  and  will 
be  foreshortened,  as  shown  by  Fig.  32,  so  that  its  appar- 
ent height  is  less  than  its  width.     The  edge  EF  is  farther 

1  Illustrators  and  artists,  even  the  most  noted,  have  made  "parallel 
perspective  "  drawings  from  the  earliest  periods.  The  influence  of  the 
many  strong  painters  who  have  used  one  vanishing-jioint  when  there 
was  no  reason  for  not  drawing  what  was  seen,  and  making  use  of  two 
vanishing-points,  probnl)ly  accounts  in  large  part  for  the  frequent  errors 
of  the  illustrators  of  the  present  time. 


%  FREE-HAND  DRAWING. 

Q 

from  the  eye,  and  appears  shorter  than  the  edge  GH. 
It  appears  the  length  of  1-2.  (This  distance  may  be 
found  by  means  of  a  plan  of  the  cube,  the  picture  plane, 
and  the  eye.)  Connecting  i-G  and  2-H,  the  vertical 
edges  are  represented  by  inclined  lines.  This  is  not  satis- 
factory. The  model  drawing  must  represent  vertical  edges 
by  vertical  lines.  If  verticals  are  drawn  from  G  and  H, 
the  front  face  will  seem  too  wide  ;  if  from  i  and  2,  it  will 
seem  too  narrow.  The  proper  effect  will  be  given  by 
verticals  between  these  lines,  or  by  verticals  from  G  and 
H,  the  line  1-2  being  dropped  a  little. 

The  model  drawing  is  not  the  exact  drawing  upon  the 
inclined  plane,  but  this  drawing  corrected  by  substituting 
vertical  for  inclined  lines. 

Figure  33.  The  cube  with  its  vertical  faces  at  45°  to 
the  picture  plane,  the  top  being  on  the  level  of  the  eye. 

The  top  is  seen  as  a  horizontal  line.  The  sides,  since 
at  equal  angles  with  the  picture,  appear  of  equal  width, 
and  the  edges  A  and  B  vanish  upward  at  equal  angles 
which  depend  upon  the  distance  of  the  eye.  When  hori- 
zontal lines  are  at  angles  of  4=;°  with  a  vertical  picture 
plane,  the  distance  of  their  vanishing-points  from  the 
centre  of  the  picture,  (that  is,  line  E,)  is  the  same  as  the 
distance  of  the  eye  from  the  picture  plane. 

The  entire  width  of  the  appearance  is  the  perspective  of 
the  diagonal  1-2  of  the  base  of  the  cube,  which  is  "  not 
foreshortened."      This  line  is  behind  the  picture  plane, 

(y&tnrt     OcH  .^3^    ^^^M     "yy^^  ^a^^^i^ire    /F/T     '*' 


T/6^    Wi^^^^ 


T^/a  XXX ci^ 


L^i^f^L  of  ^y^ 


^•^fS 


*^ /itd/toMjejC  £*A^  X  y 


Z.s^£i    o^  ^yi^ 


^^ 


Figure  34.  The  cube,  with  its  lower  face  on  the  level 
of  the  eye,  and  its  vertical  faces  extending  to  the  left  at 
30°,  and  to  the  right  at  60°. 

The  left  face  is  nearest  parallel  to  the  picture  plane, 
and  thus  appears  wider  than  the  right  face.  The  edges 
A  and  B  vanish  downward  at  angles  which  depend  on 
the  distance  of  the  eye  from  the  object,  but  the  angle  of 
A  must  always  be  less  than  that  of  B.  For  equal  dis- 
tances of  the  eye,  the  width  of  the  appearance  must  be 
less.when  the  faces  are  seen  unequally,  than  when  they 
are  seen  equally.  The  apparent  width  decreases  as  the 
cube  is  turned  toward  the  position  in  which  only  one 
side  is  seen. 

Figure  35.   The  cube  with  its  vertical  faces  vanishing 

equally,  its  top  being  four  feet  below  the  level  of  the  eye. 

/tX/  A^  ^    Here  the  sides  aj)pear  of  equal  width,  and  the  "  angles 


tf^fH 


c 

( 

-71 

\ 

V 

t< 

^^'' 

"  ^\ 

y^ 

A 

\ 

y^ 

;  ^ 


Jlc^..^.^^  /^  ^"^  ^'^^^^ 


verticals  between  these  lines,  ui  uy  ,v.»cicajb  uum  ^  _.. 
H,  the  line  1-2  being  dropped  a  little. 

The  model  drawing  is  not  the  exact  drawing  upon  the 
inclined  plane,  but  this  drawing  corrected  by  substituting 
vertical  for  inclined  lines. 

Figure  ^^.  The  cube  with  its  vertical  faces  at  45°  to 
the  picture  plane,  the  top  being  on  the  level  of  the  eye. 

The  top  is  seen  as  a  horizontal  line.  The  sides,  since 
at  equal  angles  with  the  picture,  appear  of  equal  width, 
and  the  edges  A  and  B  vanish  upward  at  equal  angles 
which  depend  upon  the  distance  of  the  eye.  When  hori- 
zontal lines  are  at  angles  of  4^°  with  a  vertical  picture 
plane,  the  distance  of  their  vanishing-points  from  the 
centre  of  the  picture,  (that  is,  line  E,)  is  the  same  as  the 
distance  of  the  eye  from  the  picture  plane. 

The  entire  width  of  the  appearance  is  the  perspective  of 
the  diagonal  1-2  of  the  base  of  the  cube,  which  is  "not 
foreshortened."      This  line  is  behind  the  picture  plane, 

(y&mrt    CcH  ^i^   S^^M    <>yi^^  c^^^^^^xrC    /f /T    ''' 


PERSPECTIVE  PRINCIPLES. 


97 


and  so  does  not  appear  its  real  length.  The  exact 
length  can  be  obtained  by  setting  off  the  actual  length  of 
the  diagonal  on  a  horizontal  line  through  the  lower  end  of 
the  front  edge,  and  by  drawing  from  its  ends,  lines  to  the 
point  opposite  the  eye.  The  intersections  of  these  lines 
with  the  lower  lines  of  the  drawing  give  the  lower  ends 
of  the  side  verticals. 

Any  known  length  can  thus  be  measured  on  the  pic- 
ture plane,  and  carried  into  the  picture  by  means  of 
parallel  lines,  which  vanish  at  C,  the  point  opposite  the 
eye. 

Figure  34.  The  cube,  with  its  lower  face  on  the  level 
of  the  eye,  and  its  vertical  faces  extending  to  the  left  at 
30°,  and  to  the  right  at  60°. 

The  left  face  is  nearest  parallel  to  the  picture  plane, 
and  thus  appears  wider  than  the  right  face.  The  edges 
A  and  B  vanish  downward  at  angles  which  depend  on 
the  distance  of  the  eye  from  the  object,  but  the  angle  of 
A  must  always  be  less  than  that  of  B.  For  equal  dis- 
tances of  the  eye,  the  width  of  the  appearance  must  be  • 
less.when  the  faces  are  seen  unequally,  than  when  they 
are  seen  equally.  The  apparent  width  decreases  as  the 
cube  is  turned  toward  the  position  in  which  only  one 
side  is  seen. 

Figure  35.    The  cube  with  its  vertical  faces  vanishing 

equally,  its  top  being  four  feet  below  the  level  of  the  eye. 

tX/  l*t  ^    Here  the  sides  appear  of  equal  width,  and  the  "  angles 


\f^7H 


A.^^^^^  ^^  ^'^  ""-^ 


98  FREE-HAND   DRAWING. 

of  inclination  "  and  convergence  are  alike  on  each  side  of 
the  central  edge.  There  are  four  parallel  edges  extend- 
ing to  the  right,  and  four  to  the  left.  Parallel  horizontal 
lines  appear  to  converge  toward  a  point  on  the  level  of 
the  eye,  and  there  will  be  two  vanishing-points.  Since 
the  edges  are  at  equal  angles  with  the  picture,  they  will 
incline  at  equal  angles,  and  the  vanishing-points  will  be 
equi-distant  on  each  side  of  the  central  edge. 

In  this  position  of  the  square,  which  is  the  base  of  the 
cube,  one  diagonal,  1-2,  is  parallel  to  the  picture  ("  not 
foreshortened ")  and  appears  a  horizontal  line.  The 
other  diagonal,  3-4,  appears  a  vertical  line,  and  the 
farther  angle  of  the  square  seems  directly  over  tlie  nearer 
one.  When  the  top  of  the  cube  is  seeji  in  this  way,  the 
visible  sides  always  appear  of  equal  7iniith. 

The  diagonals  are  perpendicular  to  each  other,  and  it 
is  seen  that  if  two  lines  are  perpendicular  to  each  other, 
and  one  is  "  not  foreshortened,"  the  right  angles  appear 
right  angles. 

Figure  36.  The  cube  above  the  eye,  its  horizontal 
edges  extending  to  the  left  at  60°,  and  to  the  right  at 

30°. 

Both  sets  of  edges  vanish  at  points  in  a  horizontal  line 
at  the  level  of  the  eye  (called  the  horizon),  the  point  at 
the  left  being  nearest  to  the  drawing,  for  the  line  at  the 
greatest  angle  7vith  the  picture  appears  the  shortest.  The 
diagonals  of  the  horizontal  surfaces  vanish.     IViint  2  is 


99 

left.  The 
to  be  its 

-2,  on  the 
"ounci,  the 
tical  face 

when  the 
45°  to  the 
)e  vertical 
s  directly 
1  I  and  2 
jisect  the 
ht  at  the 
spectively 
earer  end 
I  vanishes 
ling-point, 
ines. 

below  the 
aring  the 

It  is  thus 
.  and  the 
nish  more 
;han  those 


\\ 


^ 


PERSPECTIVE  PRINCIPLES.  99 

the  nearer  end  of  1-2,  which  vanishes  to  the  left.  The 
other,  3-4,  vanishes  to  the  right,  for  3  is  seen  to  be  its 
nearer  end. 

Figure  37.  The  cube  resting  on  an  edge,  1-2,  on  the 
ground,  with  four  of  its  faces  at  45°  to  the  ground,  the 
eye  being  above  tlie  object,  and  the  right  vertical  face 
being  visible. 

The  edge  on  the  ground  vanishes  to  the  left,  when  the 
right  vertical  face  is  seen.  If  four  faces  are  at  45°  to  the 
ground,  the  diagonals  of  the  other  faces  must  be  vertical 
and  horizontal  lines.  The  ujiper  edge,  3-4,  is  directly 
over  the  edge  on  the  ground,  and  verticals  from  i  and  2 
contain  3  and  4.  The  horizontal  diagonals  bisect  the 
vertical  diagonals,  and  vanish  toward  the  right  at  the 
level  of  the  eye.  Points  5,  6,  and  7,  8,  are  perspectively 
equi-distant  from  the  vertical  diagonals.  The  nearer  end 
of  5-3  is  5.  This  line  vanishes  upward,  and  5-1  vanishes 
downward.  Parallel  lines  have  the  same  vanishing-point, 
and  the  other  oblique  edges  vanish  with  these  lines. 

Figure  38,  A  cube  resting  on  the  ground,  below  the 
eye,  with  its  vertical  faces  visible  and  appearing  the 
widths  AB  and  AC. 

The  face  AC  appears  narrower  than  AB.  It  is  thus 
at  a  greater  angle  with  the  picture  than  AB,  and  the 
horizontal  edges  extending  to  the  right  must  vanish  more 
(luickly,  and  at  greater  "  angles  of  inclination  "  than  those 
extending  to  the  left. 


100  FREE-HAND  DRAWING. 

The  Right  Square  Pyramid. 

The  axis  of  this  pyramiil  is  perpendicular  to  the  base 
at  its  centre.  This  point  is  found  by  drawing  the  diag- 
onals. 

Figure  39.  When  the  base  of  the  pyramid  is  horizon- 
tal, the  drawing  may  be  tested  by  a  vertical  line  from 
the  centre  of  the  base.  This  should  contain  the  vertex 
of  the  pyramid. 

When  two  sides,  AB  and  CD,  of  the  base  are  "  not 
foreshortened,"  they  appear  peri)endicular  to  the  axis, 
and  one  side  only  of  the  pyramid  is  seen  if  it  is  long  or 
if  it  is  above  the  eye.  (Fig.  39.)  If  the  axis  is  short  or 
wholly  below  the  eye,  three  of  the  triangular  faces  will  be 
visible,  the  two  outer  ones  appearing  alike.     (Fig.  40.) 

One,  two,  three,  or  four  sides,  or  the  base  with  one, 
two,  or  three  sides,  may  be  visible  at  one  time. 

Figure  41.  When  two  sides  are  seen,  all  the  edges  of 
the  base  appear  to  vanish.  When  two  sides  appear 
alike,  the  edges  vanish  at  equal  angles.  The  farther 
slant  edge  is  just  behind  the  nearer.  One  diagonal  of 
the  base,  3-4,  appears  to  coincide  with  the  axis  of  the 
pyramid,  and  the  other,  1-2,  appears  at  right  angles 
to  it. 

Figure  42.  When  two  sides  are  seen  unequally,  the 
axis  of  the  pyramid  appears  perpendicular  to  a  line  which 
is  parallel  to  the  picture  plane.     A  plan  of  the  base  and 


N  - 


/ 

\ 

»h 

h- 

SN 

> 

^ 

^S^ 

^ 

w 


T/^  ^/ 


PERSPECTIVE   PRINCIPLES.  101 

the  picture  plane  will  show  the  position  of  the  line  ab 
with  reference  to  points  i  and  2.  It  passes  behind  2,  the 
nearer  point,  and  in  front  of  i,  the  farther  point.  When 
the  pyramid  is  vertical,  ab  appears  horizontal.  When 
oblique,  as  in  Fig.  43,  the  line  ab  has  the  same  relative 
position,  passing  in  front  of  the  farther  angle  of  the  base 
I,  and  behind  the  nearer  angle  2. 


The  Triangle,  and  the  Triangular  Prism. 

^^  Figure  44.  When  the  triangle  is  ecjuilateral  or  isosceles, 
and  its  base  is  a  horizontal  line,  the  altitude  of  the  tri- 
angle is^  a  vertical  line,  and  intersects  the  centre  of  the 
base. 

Figure  45.  When  neither  end  of  the  prism  is  seen,  its 
long  edges  are  "  not  foreshortened,"  and  must  be  repre- 
sented by  parallel  lines.  Points  i  and  2  are  in  perpen- 
diculars to  the  long  edges,  passing  through  the  perspective 
centres  3  and  4,  of  the  lower  edges  of  the  triangles. 

Figure-  46.  When  an  end  is  seen  with  two  sides  which 
appear  alike,  one  edge.  A,  of  the  base  is  "  not  foreshort- 
ened." The  central,  B,  of  the  receding  edges  appears  at 
right  angles  to  this  edge,  and  the  end  does  not  appear  its 
real  shape. 

Figure  47.  When  an  end  and  a  side  are  seen,  the 
drawing  may  be  tested  by  a  vertical  line  through  point  i . 
This  vertical  should  intersect  2-3,  nearer  3  than  2,  for 


102  FREE-HAND   DRAWING. 

the  nearer  half  of  any  retreating  line  appears  longer 
than  the  farther  half.  The  edges  of  the  end  vanish  in 
the  direction  of  their  farther  points,  which  are  at  once 
seen  except  in  the  case  of  the  edge  1-2.  If  line  3-7 
appears  to  intersect  the  centre  of  1-2,  edge  1-2  is  "  not 
foreshortened  "  and  does  not  vanish.  If  3-7  intersects 
1-2  nearer  2  than  i,  point  2  is  the  nearer  end  of  the  edge 
1-2.  If  3-7  intersects  1-2  nearer  i  than  2,  point  i  is 
the  nearer  end. 

The  prism  is  so  placed  that  the  edges  of  the  face  on 
the  ground  are  at  equal  angles  with  the  picture.  The 
length  of  the  prism  is  twice  that  of  the  edge  of  its  base. 
The  edges  2-3  and  2-6  vanish  at  ecjual  "  angles  of  incli- 
nation." The  nearer  half  of  2-6  appears  as  long  as  2-3, 
the  farther  half,  a  little  shorter  than  the  nearer. 


The  Regular  Hexagon. 

In  the  hexagon  there  are  four  sets  of  parallel  lines,  as 
A,  B,  C,  and  1),  in  Fig.  48.  Its  diagonal,  0-4,  is  divided 
into  four  equal  parts  by  the  diameters  D  and  the  diagonals 
B  and  C.  A  drawing  of  this  form  will  be  tested  by  seeing 
that  the  parallel  lines  vanish  in  the  directions  of  their  far- 
ther ends,  and  that  the  diameters  intersect  the  diagonal 
so  that  the  points  in  it  are  perspectively  equi-distant. 

Figure  48  represents  the  hexagon  when  its  centre  is  at 
the  level  of  the  eye,  and  it  is  "  not  foreshortened." 


PERSPECTIVE  PRIXCIPLES.  103 

Figure  49  represents  the  plane  after  it  has  been  revolved 
away  from  the  spectator  about  angle  o.  A  vertical  line, 
the  real  length  of  a  diameter,  through  o,  will  be  a  side 
of  the  rectangle  shown  in  Fig.  48  enclosing  the  figure. 
The  receding  sides  of  this  rectangle  vanish  at  the  level 
of  the  eye.  The  farther  side  is  a  vertical  through  4, 
whose  position  is  determined  by  comparing  the  apparent 
width  of  the  foreshortened  figure  with  its  height.  The 
diagonals  of  the  rectangle  give  the  centre  of  the  hexa- 
gon. A  vertical,  b,  through  the  centre,  bisects  the 
rectangle,  and  diagonals  from  b  \.o  o  and  4  give  points 
5  and  6  in  the  diameters  of  the  hexagon.  The  di- 
ameters intersect  the  sides,  giving  the  length  of  the 
sides  A. 

Figure  50  represents  the  hexagon  in  the  same  position 
as  Fig.  48,  except  that  a  diagonal  is  vertical. 

Figure  5 1  represents  the  foreshortened  hexagon,  when 
revolved  back  about  side  A.  The  enclosing  rectangle  is 
drawn  as  in  Fig.  49.  Its  diagonals  give  the  centre  of  the 
hexagon,  through  which  passes  the  diagonal  parallel  to 
side  A.  Its  ends,  o  and  4,  are  angles  of  the  hexagon. 
The  vanishing  lines  D,  from  the  nearer  side  A,  give  the 
farther  side. 

Figure  52.  The  hexagon  having  been  sketched  from 
the  object,  to  test  the  drawing  (assuming  the  diameter 
AB  to  be  correctly  placed), — 

Draw  CD,  which  will  be  horizontal,  (parallel  to  AB,) 


104  FREE-HAND  DRAWING. 

when  point  4  appears  over  o.  Draw  AD  and  BC.  See 
that  o-i  is  greater  than  1-2  and  3-4  less  than  2-3. 

Figure  53.  To  test  the  sketch  (assuming  the  nearest 
side  to  be  correctly  placed), — 

Draw  the  diameters  AC  and  BD,  and  the  diagonals 
AD  and  BC,  giving  point  2.  Through  2  draw  0-4.  See 
that  the  points  on  this  line  are  equi-distant,  actually  equi- 
distant when  the  line  is  "  not  foreshortened,"  and  per- 
spectivdy  so  when  the  line  vanishes. 

The  Hexagonal  Prism  and  Pyramid. 

Figure  52  may  represent  the  top  of  a  vertical  prism, 
two  of  whose  sides  will  be  seen  equally  when  4  appears 
just  over  o.  The  side  o-A  inclines  at  the  same  angle  as 
o-B,  at  both  the  top  and  the  bottom  of  the  prism,  though 
the  angles  of  the  lower  lines  are  greater  than  those  of  the 
upper.  When  two  sides  are  seen  equally  and  the  prism 
is  not  vertical,  the  directions  of  the  lines  o-A  and  o-B  may 
be  determined  by  means  of  the  diameters  AB  and  CD 
of  the  hexagon,  which  appear  perpendicular  to  the  axis 
of  the  prism. 

Figure  53  may  represent  the  top  of  the  prism  when 
three  of  its  vertical  faces  are  seen,  the  two  outer  ones 
appearing  of  equal  width.  When  thus  seen,  the  edges 
AB  and  CD  of  the  ends  appear  perpendicular  to  the 
axis  of  the  prism. 


PERSPECTIVE  PRINCIPLES.  105 

Figure  54  represents  the  prism  when  three  faces  appear 
of  unequal  widths.  The  narrower  A  is  the  farthest  from 
the  eye.  Points  a  and  c  are  thus  farther  from  the  eye 
than  b  and  d,  and  ab  and  cd  vanish  to  the  left.  The 
parallel  horizontal  lines  of  the  ends  vanish  in  four  points, 
which  must  be  the  same  distance  above  the  drawmg  (at 
the  level  of  the  eye).  The  equal  spaces  on  0-4  appear 
unequal.  The  vanishing  of  the  parallel  lines  brings  tlie 
lower  base  of  the  proper  width,  it  being  greater  in  this 
case  than  tiiat  of  the  top.  The  invisible  end  of  a  prism 
may  appear  wider  or  narrower  than  the  visible  end  (see 
page  in). 

Figure  55  represents  a  prism  whose  length  is  twice  that 
of  the  diagonal  of  its  base.  The  prism  rests  on  one  face 
on  the  ground,  and  is  below  the  eye.  The  edges  of  this 
face  are  at  ei[ual  angles  with  the  picture. 

The  diameters  of  the  ends  are  vertical  lines  and  with 
the  diagonals  ab  and  tv/,  give  points  i,  2,  3,  etc.,  which 
are  perspectively  equi-distant.  The  narrower  face  A  is 
the  more  distant,  point  a  is  the  farther  end  of  o-a  and 
the  edge  vanishes  upward.  The  "  angle  of  inclination  " 
of  bd  is  the  same  as  that  of  df.  The  side  0-5  is  per- 
spectively twice  as  long  as  the  diagonal  0-4.  To  fully 
test,  draw  the  invisible  edges,  and  the  diameters  and  the 
diagonals  of  the  bases.  Continue  all  parallel  lines  to  see 
that  they  vanish  toward  one  point. 

The  question  may  arise  "  Shall  the  nearer  half  of  the 


106  FREE-HAND  DRAWING. 

diameter  ad,  be  represented  by  a  greater  distance  than 
the  farther  half?"  ;  omitting  the  convergence  of  the  ver- 
tical lines  makes  the  ecjual  distances,  ac  and  r</,  equal  in 
the  drawing. 

Figures  56  and  57.  The  tests  for  the  pyramid  are  the 
same  as  for  the  prism  and  the  square  pyramid,  ^^'hen 
three  faces  are  seen,  the  outer  ones  equally,  the  axis 
appears  perpendicular  to  a  diagonal  of  the  base.  When 
two  fac6s  appear  equal,  the  axis  appears  perpendicular 
to  a  diameter.  When  two  or  three  are  seen  unequally,, 
the  axis  appears  perpendicular  to  a  line  between  the 
diameter  and  the  diagonal,  as  in  Fig.  42. 

The   Circle. 

The  circle  appears  its  real  shape  when  it  is  "  not 
foreshortened,"  and  this  means  any  position  in  which  the 
circle  is  seen  in  a  direction  perpendicular  to  the  circle  at 
its  centre.  It  appears  a  straight  line  when  the  eye  is  in 
the  plane  of  the  circle.  In  other  positions,  in  which  its 
entire  circumference  is  seen,  it  appears  an  ellipse.  If 
we  suppose  the  picture  plane  to  be  a  plane  surface,  the 
cone  of  visual  rays  will  be  intersected  by  it  in  a  perfect 
ellipse,  but  if  we  suppose  the  picture  plane  to  be  a  sphere 
or  other  curved  surface,  the  section  will  not  be  an  ellipse ; 
practically,  the  circle  appears  an  ellipse. 

Figure   58    is   an   elevation   rei)resenting   the    eye,   a 


PERSPECTIVE   PRINCIPLES.  107 

horizontal  circle  C  on  the  level  of  the  eye,  and  other  cir- 
cles, A,  B,  D,  and  E,  above  and  below  the  level  of  the  eye. 

Figure  59  is  a  plan  of  the  same.  The  circles  are 
tangent  to  a  vertical  picture  plane.  In  the  elevation, 
lines  to  the  ends  of  the  horizontal  lines  representing  the 
circles,  represent  the  visual  rays,  by  which  their  appar- 
ent heights  are  seen.  These  rays,  intersecting  the  pict- 
ure plane,  give  the  short  axes  of  the  ellipses  of  Fig.  60. 
In  the  plan,  the  lines  tangent  to  the  circle  represent  visual 
rays,  and  intersecting  the  picture  plane  at  i  and  2,  they 
give  the  length,  1-2,  of  the  long  axes  seen  in  Fig.  60. 

As  the  circle  is  dropped  or  lifted  from  the  level  of  the 
eye,  the  length  of  the  short  axis  increases,  and  within 
ordinary  limits  this  is  true  of  the  appearance  of  all 
horizontal  circles. 

Figure  61  represents  a  square,  two  of  whose  sides  are 
"  not  foreshortened."  A  circle  inscribed  in  the  square 
must  be  represented  by  an  ellipse,  tangent  to  the  square  at 
its  diameters  in  points  i,  2,  3,  and  4.  The  centre  of  the 
square  is  at  the  intersection  of  its  diagonals,  and  appears 
nearer  2  than  i.  The  centre  of  the  square,  that  is,  the 
centre  of  the  circle,  is  not  the  centre  of  the  ellipse.  In 
other  words,  the  diameter  of  the  circle  does  not  appear 
as  long  as  a  chord  in  front  of  the  diameter,  and  the  long 
axis  of  the  ellipse  is  not  a  diameter  of  the  circle. 

Figure  62  is  an  elevation  representing  the  eye,  the 
picture  plane,  and  the  ground,  with  the  circle  upon  it. 


108  FREE-HAND  DRAWING. 

Figure  63  is  a  plan  of  the  same,  both  views  correspond- 
ing with  Fig.  61.  The  visual  rays  r,  r,  to  points  i  and  2, 
determine  at  the  picture  plane  the  short  axis  of  the 
ellipse.  The  line  P,  bisecting  the  angle  between  the 
rays,  gives  the  centre  of  the  ellipse,  and  continued  to 
the  ground,  gives  the  position  of  the  chord  MN,  which 
appears  the  longest  line  of  the  circle. 

The  eye  is  above  the  ground,  and  thus  in  the  plan,  the 
visual  rays  r,  r  do  not  come  tangent  to  the  circle  at 
points  M  and  N. 

All  lines  whose  ends  are  unequally  distant  must  appear 
to  vanish.  In  any  circle  there  can  be  but  one  diameter 
which  is  "  not  foreshortened."  This  is  the  one  which  is 
perpendicular  to  the  direction  in  which  the  circle  is  sten. 

Such  a  horizontal  line  appears  horizontal,  and  thus  a 
horizontal  circle  always  appears  a  horizontal  ellipse,  for 
though  the  diameter  does  not  appear  the  long  axis  of  the 
ellipse,  it  is  parallel  to  the  chord  which  appears  the  long 
axis,  and  this  chord  is  thus  "  not  foreshortened." 

The  short  axis  of  an  ellipse  is  perpendicular  to,  and 
bisects  the  long  axis.  The  short  diameter  of  the  ellijrse 
aj)pears  a  vertical  line  in  the  case  of  a  horizontal  circle, 
and  in  any  circle  appears  to  coincide  with  a  line  per- 
pendicular to  the  circle  at  its  centre. 

Conversely,  the  long  axis  of  any  ellipse  appears  per- 
pendicular to  a  line  which  is  at  right  angles  to  the  plane 
of  the  circle  at  its  centre. 


PERSPECTIVE  PRINCIPLES.  109 

Figure  64.  The  vertical  circle  A,  when  its  centre  is 
on  the  level  of  the  eye,  appears  a  circle,  or  an  ellipse 
whose  long  axis  3-4  is  vertical,  for  a  horizontal  line  on 
the  level  of  the  eye  appears  horizontal,  and  this  line 
determines  the  direction  of  the  long  axis  of  the  ellipse. 

B  and  C  are  vertical  circles  of  the  same  size  as  A, 
directly  over  and  under  A,  and  in  the  same  plane. 
Horizontal  lines,  perpendicular  to  these  circles  at  their 
centres,  vanish  at  the  level  of  the  eye.  These  lines 
determine  the  directions  of  the  long  axes  7-8  and 
11-12  of  the  ellipses  which  represent  B  and  C,  and  it  is 
seen  that  the  axis  of  an  ellipse  7vhich  represents  a  verti- 
cal, foreshortened  circle,  on  any  level  except  that  of  the 
eye,  must  be  an  inclined  line. 

The  circles,  being  of  the  same  size  and  in  the  same 
vertical  plane,  will  be  tangent  to  two  vertical  lines  which 
are  represented  by  vertical  lines  R  and  S.  In  order 
that  the  upper  and  lower  ellipses  shall  be  tangent  to 
R  and  S,  their  short  axes,  5-6  and  9-10,  must  be  shorter 
than  1-2,  that  of  the  central  ellipse.  The  width  of  the 
ellipse  decreases  as  a  vertical  circle  is  raised  or  lowered. 

The  long  axes  7-8  and  ri-12  appear  a  little  shorter 
than  3-4.  ^^'hether  this  difference  shall  be  represented 
or  not  is  a  question  similar  to  that  considered  on 
page  51. 


110  FREE-HAND  DRAWING. 

The  Cylinder. 

When  an  end  only  is  seen,  it  is  "  not  foreshortened," 
and  appears  its  real  shape.  If  an  end  and  the  cur\'ed 
surface  are  seen,  the  end  is  foreshortened,  and  appears 
an  ellipse.  Less  than  half  the  curved  surface  of  the 
cylinder  can  be  seen  at  one  time. 

Figure  65.  When  one  end  of  the  cylinder  appears  a 
straight  line,  the  other  appears  an  ellipse,  B. 

When  neither  end  surface  is  visible  as  a  straight  line, 
or  as  a  surface,  both  ends  appear  narrow  ellipses.  The 
cylinder  A  is  then  "  not  foreshortened." 

When  one  end  of  a  vertical  cylinder  is  visible,  the 
other  is  invisible,  and  appears  a  wider  ellipse  than  the 
visible  end  (see  C  and  D). 

The  elements  of  a  vertical  cylinder  appear  to  converge 
when  the  cylinder  is  not  on  the  level  of  the  eye,  but  are 
represented  by  vertical  lines. 

The  long  axis  of  the  ellipse  representing  any  circle  is 
perpendicular  to  a  line  which  is  at  right  angles  to  the  cir- 
cle at  its  centre.  In  the  cylinder  this  line  is  its  axis, 
and  in  any  drawing  of  the  cylinder  the  long  axes  of  the 
ellipses  must  always  be  at  right  angles  to  the  axis  of 
the  cylinder.  Generally,  the  fact  that  the  centre  of  the 
ellipse  is  not  the  centre  of  the  circle  may  be  disregarded, 
and  the  line  connecting  the  centres  of  the  ellipses  be  con- 
sidered the  axis  of  the  solid. 


PERSPECTIVE  PRINCIPLES.  Ill 

The  visible  end  of  any  cylinder  is  nearer  the  eye  than 
the  invisible,  which  must  thus  appear  smaller  than  the  visi- 
ble. The  elements  connecting  the  two  ends  appear  to 
converge,  as  any  parallel  lines.  The  question  of  the  com- 
parative widths  of  the  visible  and  the  invisible  ends  has 
caused  much  trouble.  Figures  22  and  23  show  that  the 
widths  are  dependent  upon  the  position  of  the  cylinder. 
When  it  is  at  an  angle  less  than  45°  with  the  picture,  the 
invisible  base  appears  the  wider,  as  in  the  vertical  cylin- 
der as  generally  seen.  When  the  cylinder  is  at  a  greater 
angle  than  45°  with  the  picture,  the  invisible  base  appears 
the  narrower.  This,  however,  is  not  exact  for  angles  near 
45°,  and  refers  to  common  positions  of  the  object.  For 
unusual  conditions,  as  a  very  long  object  near  the  spec- 
tator, or  for  a  number  placed  in  a  line  extending  for 
some  distance,  it  cannot  apply ;  as  the  distortion  caused 
by  the  use  of  any  one  picture  plane  would  then  be  very 
great.  It  is  best  not  to  attempt  to  draw  an  object  which 
is  so  near  as  to  create  a  visual  angle  of  over  30°. 

Figure  66.  The  invisible  base  A  is  always  at  a  less 
angle  to  the  plane  which  gives  the  appearance  than  the 
visible  B ;  that  is,  the  visual  rays  to  the  invisible  base 
make  greater  angles  with  it  than  those  made  by  the  vis- 
ual rays  to  the  visible  base.  The  invisil)le  base  is  nearer 
to  the  position  in  which  it  is  "  not  foreshortened  "  than 
the  visible,  and  though  it  appears  narrower  than  the 
visible  base,  when  the  cylinder  is  at  a  greater  angle  than 


112  FREE-HAND  DRAWING. 

45°,  it  also  appears  shorter,  and  always  appears  propor- 
tionally wider  than  the  visible.  This  is  the  only  rule  tliat 
can  be  given.  The  difference  between  the  apparent  sizes 
depends  upon  the  distance  of  the  eye,  and  decreases  as 
the  distance  increases.  When  the  distance  of  the  eye  is 
short,  the  difference  is  marked. 

Figure  67  represents  a  horizontal  cylinder  on  the  level 
of  the  eye.  The  cylinder  extends  to  the  left  at  45°  with 
the  picture,  and  its  base  extends  to  the  right  at  the  same 
angle.     Its  length  is  twice  its  diameter. 

The  short  axis  1-2  of  the  visible  end  A  is  a  perspec- 
tive half  of  the  element  1-3.  The  contour  elements  con- 
verge toward  the  left. 

Figure  68  represents  the  same  cylinder,  still  at  45°  to 
the  picture,  but  inclining  upward  to  the  right  instead  of 
being  horizontal. 

The  appearance  is  the  same  as  that  in  P'ig.  67,  An 
object  at  an  angle  with  the  picture  will  present  the  same 
appearance  as  long  as  this  angle  is  unchangetl.  It  may  re- 
volve through  a  circle,  and  the  only  change  is  in  the  posi- 
tion of  the  appearance  with  reference  to  a  horizontal  line. 

Figures  69  and  70  represent  horizontal  cylinders  B  and 
C,  respectively  over  and  under,  and  the  same  size  as  the 
horizontal  cylinder  A  in  Fig.  67,  which  is  here  repre- 
sented by  dotted  lines.  The  ends  are  circles  situated  as 
those  in  Fig.  64,  and  the  ellipses  representing  them  must 
be  tangent  to  two  vertical  lines. 


PERSPECTIVE  PRLXCIPLES.  113 

Figure  71  represents  a  horizontal  cylinder  below  the 
eye,  and  extending  directly  away  from  the  spectator  so 
that  its  axis  appears  a  vertical  line. 

The  end  appears  an  ellipse,  whose  long  axis  being  at 
right  angles  to  the  axis  of  the  cylinder  is  a  horizontal 
line.  The  tendency  is  to  represent  the  end  by  a  circle 
but  it  can  appear  so  only  when  no  part  of  the  cur\'ed 
surface  is  seen. 

Figure  72  represents  a  cylinder  of  the  same  size  and 
parallel  to  that  of  Fig.  71,  the  ends  of  the  cylinders 
being  in  the  same  planes. 

In  Fig.  71  the  elements  converge  on  the  level  of  the 
eye.  To  this  point  the  axis  and  elements  of  the  parallel 
cylinder  appear  to  extend.  The  centres  of  the  ends  are 
best  represented  by  points  in  horizontal  lines  through  the 
centres  of  the  ends  of  the  first  object.  The  long  axes  of 
the  ellipses  pass  through  these  points  perpendicular  to 
the  axis  of  the  cylinder.  The  short  axes  will  be  shorter 
than  those  of  Fig.  71,  for  the  ellipses  must  be  tangent  to 
horizontal  lines,  which  are  tangent  to  the  ellipses  of 
Fig.  71. 

The   Cone. 

The  cone  appears  a  circle  when  its  axis  would  appear 
a  point  ;  a  triangle,  when  its  base  is  seen  as  a  straight 
line.  The  entire  curved  surface  is  visible  when  the 
cone  points   toward   the    eye ;    none   of  the  curved  sur- 


114  FREE-HAND   DRAWING. 

face  is  seen  when  the  cone  points  directly  away  from 
the  eye.  Between  these  positions  any  part  of  the 
curved  surface  may  be  visible,  the  circle  appearing  an 
ellipse. 

The  Ifese  of  the  cone  being  at  right  angles  to  the  axis 
as  in  the  cylinder,  it  appears  an  ellipse  whose  long  axis  is 
perpendicular  to  the  axis  of  the  cone.  The  contour  ele- 
ments must  appear  tangent  to  the  ellipse  of  the  base. 

Figure  73  represents  three  cones  of  the  same  size, 
A,  B,  and  C,  on  a  horizontal  surface  below  the  eye. 

Cone  A  is  vertical.  The  long  axis  of  the  ellipse  of 
the  base  appears  horizontal.  The  contour,  elements  are 
tangent  to  the  ellipse  above  its  long  axis,  showing  that 
more  than  half  of  the  ellipse  represents  the  visible  edge 
of  the  base. 

Cone  B  rests  on  an  element  on  the  ground.  The 
base  is  visible,  and  appears  wider  than  that  of  A.  The 
axis  thus  appears  shorter  than  that  of  A,  and  noting 
the  tangent  points  of  the  elements,  we  see  that  less  than 
half  the  curved  surface  is  seen. 

Cone  C  inclines  toward  the  spectator.  Its  base 
appears  wider  and  its  axis  shorter  than  that  of  B.  Much 
more  than  half  the  curved  surface  is  seen. 

To  draw  the  cone,  cylinder,  or  any  similar  object, 
the  methods  explained  on  page  33  should  be  followed. 
The  mass  should  be  drawn  first,  and  visible  lines  before 
imaginary  ones.     The  axis,  (which  is  an  imaginary  line,) 


PERSPECTIVE  PRINCIPLES.  115 

should  not  be  drawn  first,  as  is  often  recommended. 
After  the  position  and  proportions  have  been  obtained, 
the  axis  may  be  indicated  as  a  test  before  the  drawing 
is  accented,  but  on  no  account  should  this  Une  be  drawn 
first. 

Concentric   Circles. 

Concentric  circles  appear  ellipses  whose  long  axes 
are  parallel,  but  since  the  centre  of  the  circle  is  not  the 
centre  of  the  ellipse,  the  long  axes  of  the  two  ellipses 
will  not  coincide. 

Figure  74  represents  in  perspective  and  half  plan 
concentric  squares  with  tangent  circles,  the  inner  ones 
being  half  the  diameter  of  the  outer. 

The  angles  of  the  inner  square  are  in  the  diagonals  of 
the  outer,  and  are  given  in  perspective  by  drawing  the 
receding  sides  of  the  inner  from  the  points  2  and  3  of 
the  half  plan.  EF  is  the  short  axis  of  the  ellipse  tangent 
to  the  larger  perspective  square.  GH,  the  short  axis  of 
the  smaller  ellipse.  The  long  axes  bi::ect  the  short,  and 
it  is  seen  that  AB,  that  of  the  larger  ellipse,  comes  in 
front  of  the  centre  of  the  square  O,  and  also  in  front  of 
IK,  the  long  axis  of  the  smaller  ellipse. 

Points  E,  G,  O,  H,  and  F  are  equi-distant  in  the 
diameter  of  the  larger  circle,  and  divide  it  into  four 
equal  spaces,  which  appear  perspectively  equal.  The 
diameter  CD  of  the  circle  is  "  not  foreshortened,"  and  > 


116  FREE-IJAXD  DRAWING. 

the  equal  divisions  upon  it  appear  equal.  The  diameter 
CD  is  not  the  long  axis  of  either  ellipse,  but  is  parallel 
to  them,  and  generally  there  is  so  little  space  between 
them  that  practically  we  may  say  that  the  ecjual  divis- 
ions on  the  diameter  of  the  circle  appear  in  the  long 
axis  of  the  ellipse,  and  if  the  distance  AI  between  the 
ellipses,  measured  horizontally,  is  one-fourth  of  the 
entire  long  axis  AB,  the  distances  EG  and  HF  are  per- 
spective foiirdis  of  the  entire  short  axis  EF. 

The  apparent  distances  at  front  and  back,  between 
ellipses  representing  concentric  circles,  are  always  the 
same  perspective  parts  of  the  entire  short  axis,  that  the 
distances  between  the  ellipses  on  the  long  axis  are  of 
the  entire  long  axis. 

The  distance  between  the  long  axes  of  the  elHpscs  is 
equal  to  one-half  the  difference  in  length  of  HF  and 
EG. 

Figure  75  represents  concentric  circles  more  nearly  ?.s 
they  generally  appear,  the  distance  FG  being  but  little 
shorter  than  AB,  and  the  long  axes  of  the  ellipses  thus 
being  very  near  together.  The  distance  5-6  is  one-sixth 
of  the  axis  0-6,  and  shows  that  the  spaces  AB  and  FG 
must  be  perspective  sixths  of  the  short  axis  AG,  The 
drawing  shows  that  the  retreating  parallel  circles  do  not 
appear  to  converge  except  beyond  the  centre  of  the  cir- 
cle. Thus,  curved  parallel  retreating  lines 'may  appear 
to  converge  or  diverge. 


PENSPE  C  77 1  'E    PKEVC/PLES.  1 1 7 

Figure  76  represents  a  circular  ring,  a  cross-section  of 
which  is  a  square. 

The  circles  are  concentric  on  each  side  of  the  ring. 
The  distance  4-8  is  actually  one-seventh  of  the  long  axis, 
and  the  distance  2-9  is  a  perspective  seventh  of  the  short 
axis.  The  square  which  is  the  section  of  the  ring  appears 
very  nearly  its  real  shape  at  the  ends,  the  horizontal 
side  4-8  appearing  a  little  longer  than  the  vertical  3-4. 
'I'he  distance  1-2  at  the  front,  is  longer  than  3-4,  anil  at 
the  back  5-6  is  a  little  shorter.  The  invisible  lines  should 
always  be  sketched,  so  that  the  lines  which  are  seen  may 
have  the  right  direction.  Care  must  be  taken  not  to 
exaggerate  the  distance  between  the  long  axes  of  the 
ellipses.  In  many  cases  it  will  not  be  necessary  to  draw 
more  than  one  line  as  a  test  for  both  ellipses. 

The  Frustum  of  the  Pyramid  and  the  Cone. 

When  any  pyramid  is  cut  by  a  plane  parallel  to  its  base, 
the  section  is  similar  to  the  base  and  the  lines  of  both 
figures  are  parallel. 

Figure  77  represents  the  frustum  of  a  square  pyramid. 
This  is  a  form  frequently  found  in  furniture,  chairs,  tables, 
etc.  The  drawings  from  these  objects  may  be  tested  by 
seeing  that  the  slant  lines,  when  continued,  meet  at  a 
point  over  the  centre  of  the  base,  and  that  the  lines  of 
the  upper  base  are  parallel  to  those  of  the  lower. 


lis  FREE-HAND   DKAIVIXG. 

Figure  78  represents  the  frustum  of  a  cone  below  the 
eye,  with  the  larger  base  A  visible. 

The  contour  elements  of  the  cone  appear  tangent  to 
the  ellipses  of  both  bases  and,  when  continued,  meet  at  a 
point  in  the  axis  of  the  cone.  The  smaller  base  is  invisi- 
ble, and  thus,  being  more  tlistant,  appears  proportionally 
wider  than  the  visible. 

Figure  79  represents  the  same  object,  but  seen  from  a 
nearer  position,  the  ellipses  appearing  wider. 

The  contour  elements  are  tangent  to  the  ellipses  forther 
from  the  ends  of  their  long  axes,  and  thus  less  of  the  con- 
vex surface  is  visible.  A  circle  A,  half-way  between  the 
two  bases,  is  represented  by  an  ellipse  tangent  to  the  con- 
tour elements,  and  perspectively  half-way  between  the 
ellipses  of  the  bases.  The  nearest  element  of  the 
cone  appears  a  vertical  line  and  extends  from  its  upper 
end  b  away  from  the  eye.  Its  centre  i  thus  appears  nearer 
a  than  b.  The  farther  element  of  the  cone  is  nearer  the 
pxDsition  in  which  it  is  "  not  foreshortened,"  and  ])oint  2 
is  practically  midway  between  c  and  d.  The  width  of 
the  ellipse  is  proportionally  greater  than  that  of  the  upper 
ellipse,  but  less  than  that  of  the  lower. 

Figure  80  represents  the  cone  with  its  smaller  base 
visible  and  a  conical  band  about  its  surface.  The  ele- 
ments are  tangent  to  the  ellipses  behind  the  ends  of 
their  long  axes,  and  more  than  half  of  the  convex  sur- 
face is  seen.     As  already  shown,  the  visible  curved  sur- 


PERSPECTIVE   PRINCIPLES.  119 

foce  oi  the  cone  may  vary  from  none  to  all.  Circles  or 
bands  about  the  convex  surface  will  be  visible  in  the  same 
proportion  as  the  surface  of  the  cone ;  less  than  half  the 
ellipses  being  seen  when  the  larger  base  of  the  cone  is 
visible,  and  more  than  half  when  it  is  invisible.  The 
apparent  thickness  of  the  ring  or  band,  at  the  short  and 
long  axes  of  the  ellipses,  is  given  by  the  test  for  concen- 
tric circles. 

Figure  8i  represents  a  frustum  of  a  cone  and  a  circle 
between  the  two  bases. 

The  apparent  width  of  bands  A  and  B  varies  with  the 
angle  of  the  cone  and  the  position  of  the  eye ;  but  this 
is  a  question  of  little  importance,  for  the  proportions  of 
the  ellipses  can  always  be  easily  determined  as  explained, 
and  the  ellipses  being  correctly  placed,  the  spaces  be- 
tween must  be  correctly  represented. 

Figure  82  represents  a  dish  of  conical  form. 

The  nearer  side  of  the  dish  is  foreshortened  more  than 
the  farther,  and  thus  appears  much  narrower.  The  rela- 
tive widths  depend  wholly  upon  the  position  of  the  eye. 
If  lifted,  the  front  appears  narrower  until  it  is  seen  edge- 
wise, and  if  farther  raised,  all  the  inner  surface  is  visible. 

An  elevation  of  the  object,  representing  the  position  of 
the  eye,  the  picture  plane,  and  the  visual  rays  will  assist 
in  obtaining  the  proportions  of  the  model  drawing  when 
it  is  made  without  the  object.  When  drawing  from  the 
object,  if  the  appearance  of  any  part  is  not  clearly  under- 


120  FREE-HAND   DRAWING. 

Stood,  this  elevation  will  often  help  to  make  th6  princi- 
ples clear. 

Figure  83  represents  a  double  cone,  composed  of 
intersecting  cones  A  and  B,  whose  bases  are  four  inches 
in  diameter,  and  whose  axes  are  six  inches.  The  whole 
length  is  eight  inches. 

The  elements  converge  to  points  in  the  axis  of  the 
double  cone,  which  are  ecjuidistant  from  the  bases  and 
from  the  intersection  of  the  two  objects.  The  smaller 
circle  is  common  to  both  cones,  and  the  ellipse  which 
represents  it  must  be  tangent  to  the  elements  of  both 
cones.  Less  than  half  the  surface  of  A  and  more  than 
half  the  surface  of  B  is  visible.  It  follows  that  the  ele- 
ments of  the  farther  cone,  B,  must  appear  to  intersect 
those  of  tlie  nearer  one,  A.  When  the  cones  are  much 
foreshortened  this  point  is  prominent,  as  in  the  sketch  at 
the  left. 


The  Torus  and  Ring  of  Circular  Section. 

The  torus  is  a  convex  moulding  frequently  found  in 
architecture,  and  in  many  common  objects. 

Figure  84.  An  easy  way  to  draw  this  form  is  to  sketch 
the  ellipses  representing  the  circles,  which  may  be  con- 
sidered its  bases.  The  section  of  the  surface  connecting 
these  bases  appears  nearly  its  real  shape  at  the  ends 
of  the  long  axes  of  the  ellipses.     (The  semicircle  in  this 


PERSPECTIVE   PRINCIPLES.  121 

position  below  the  eye  appears  half  of  a  horizontal 
ellipse.)  The  curved  contour  of  the  moulding  will  be 
represented  by  a  line  tangent  to  the  semicircle,  anil 
nearly  so  to  the  upper  and  lower  ellipses,  or,  if  the  ellipses 
are  wider,  farther  above  and  below  the  ellipses. 

Figure  85  represents  the  ring.  This  object  will  be  rep- 
resented by  concentric  circles,  when  it  is  "  not  foreshort- 
ened," but  when  foreshortened,  its  outlines  will  not  be 
ellipses.  This  is  due  to  the  fact  that  the  outer  visual  rays 
are  tangent  in  front  below  the  centre  of  the  ring,  and  be- 
hind above  the  centre.  Thus  the  line  on  the  ring  which 
is  on  the  contour  is  not  a  circle.  When  much  foreshort- 
ened, the  inner  outline  of  the  farther  part  will  pass  behind 
the  outline  of  the  nearer  part,  as  in  the  drawing. 

The  centre  line  of  the  ring  is  a  circle  which,  if  seen, 
would  appear  an  ellipse.  Suppose  a  sphere  of  the  diam- 
eter of  the  section  of  the  ring  to  move,  with  its  centre  in 
the  circle,  around  the  circle.  The  sphere  would  describe 
the  surface  of  the  ring.  The  sphere  will  be  represented 
in  all  its  positions  by  a  circle.  When  behind,  by  a  circle 
slightly  smaller  than  when  in  front.  The  outline  of  the 
ring  must  be  represented  by  a  line  tangent  to  the  circles 
representing  the  sphere.  Its  outlines  are  thus  very  nearly 
parallel  to  the  ellipse  representing  the  centre  of  the  ring. 
It  should  be  noted  that  if  a  line  is  parallel  to  an  ellipse, 
it  is  not  an  ellipse.     Parallel  ellipses  are  impossible. 


122  FREE-HAND  DRAlVli\G. 


Frames. 


In  the  frames  of  regular  shapes  are  found  concentric 
polygons.  The  angles  of  the  inner  figure  being  in  the 
diagonals  of  the  outer,  this  point  enables  us  to  test  draw- 
ings of  these  objects. 

'Figure  86  represents  a  cubical  frame. 

The  diagonals  of  any  face,  as  ABCD,  contain  the 
angles  of  the  inner  square,  any  line  of  which  being 
drawn,  gives  points  in  two  other  lines.  Any  angle  of  the 
object  is  an  end  of  three  lines.  Thus,  from  E  extend 
EF,  EG,  and  EL.  Continue  any  inner  line  to  an  outer 
edge  of  the  object,  and  a  point  in  the  continuation  of  a 
second  inner  line  is  found.  Thus,  EG  continued  to  AB 
gives  point  i,  which  is  in  IK,  and  EF  continued  to  the 
top,  gives  a  point  in  an  inner  edge  which  extends  to  the 
left. 

Figure  87  represents  an  equilateral  triangular  frame. 

The  angles  of  the  inner  triangle  are  in  perpendiculars 
to  the  centres  of  the  opposite  sides.  These  lines  inter- 
sect each  other  at  the  centre  of  the  triangle.  Any  side 
of  the  inner  triangle,  as  A,  gives  points  i  and  2  in  the 
other  sides,  B  and  C.  Any  side,  as  A,  may  be  continued 
to  the  outer  triangle,  giving  3.  From  3  a  parallel  to  the 
short  edges  gives  4,  which  is  in  the  edge  D,  parallel  to  A. 

Figure  88  represents  a  square  frame  with  a  circle  A 
tangent  to  the  inner  square. 


PERSPECTIVE  PRINCIPLES.  123 

The  student  will  probably  draw  the  long  axis  of  the 
ellipse  representing  this  circle  parallel  to  either  the  side 
or  the  diagonal  of  the  square.  The  long  axis  is  parallel  to 
the  side,  when  one  outer  side  only,  as  B,  of  the  square 
frame  is  seen.  It  is  parallel  to  the  diagonal  only  when 
two  sitles,  as  B  and  D,  are  seen  equally.  It  is  generally 
parallel  to  neither. 

The  long  axis  is  perpendicular  to  the  axis  of  the  cylin- 
der, of  which  the  circle  is  the  base.  The  direction  of  the 
axis  of  the  cylinder  is  that  of  the  short  edges  of  the 
frame.  A  parallel  to  these  lines,  through  the  centre  of 
the  square,  will  be  the  short  axis  of  the  ellipse.  The 
ellipse  is  tangent  to  the  square  at  points  a,  h,  c,  and  d  in 
vertical  and  perspectively  horizontal  lines  through  the 
centre  e.  The  long  axis  is  perpendicular  to,  and  bisects 
the  short,  and  comes  in  front  of  the  centre  of  the  square. 

Figure  8g  represents  a  reading-glass,  and  illustrates 
the  fact  shown  above,  that  the  direction  of  the  long  axis 
of  the  ellipse  must  not  be  referred  thoughtlessly  to  any 
other  lines  of  the  object. 

The  student  who  does  not  observe,  will  draw  the  long 
axis  of  the  ellipse  in  the  direction  of  the  handle  of  the 
glass.  It  may,  by  chance,  have  this  direction,  but  its 
direction  may  be  very  different.  The  handle  radiates 
from  the  glass,  as  a  spoke  from  its  hub,  and  its  direction 
may  be  that  of  any  one  of  the  many  spokes  in  the  wheel. 

Figure  90  is  an  elevation,  and  Fig.  91a  model  draw- 


124  FREE-HAND  DRAWING. 

ing  of  a  cylindrical  object  having  a  moulding  and  grooves 
about  its  surface. 

Figure  90  represents  the  picture  plane,  and  the  visual 
rays  converging  toward  the  eye.  These  rays  intersect 
the  picture  plane,  and  give  upon  it  the  positions  of  the 
various  points  to  which  they  pass. 

The  upper  form.  A,  is  that  of  the  torus,  explained  on 
page  120. 

The  central,  B,  is  the  reverse  of  this  form.  The  cir- 
cles appear  lines,  5-6  and  7-8,  in  the  elevation.  The 
rays  to  these  points  intersect  the  picture  plane,  and  give 
the  short  axes,  5-6  and  7-8,  of  the  ellipses.  The  cur\'ed 
lines  N  and  M,  if  visible,  end  above  the  long  axis  of 
the  ellipse. 

Form  C  is  that  of  the  double  cone,  explained  on 
page  120. 

Vase  Fonns. 

Figure  92  is  an  elevation  representing  the  vase  shown 
by  the  model  drawing,  Fig.  93,  in  which  a  common  mis- 
take is  shown  at  the  right  side  of  the  drawing,  where  the 
line  representing  the  body  of  the  vase  extends  to  the 
long  axis  of  the  ellipse  of  the  neck.  The  outline  of 
the  body  must  at  least  pass  tangent  to  the  ellipse,  as 
at  the  left,  and  it  may  pass  above  the  ellipse.  The 
neck  of  the  vase  thus  extends  inside  the  outline  of  the 
body. 


PERSPECTIVE  PRINCIPLES.  125 

When  the  top  of  the  vase  is  at  right  angles  to  the  axis 
its  circles  are  concentric,  and  appear  as  in  Fig.  75. 

Figure  94.  When  a  handle  projects  from  the  side  of 
the  vase,  its  thickness  breaks  the  outlines.  When  the 
liandle  extends  toward  the  eye,  the  line  of  intersection 
appears  fuller  and  more  nearly  its  real  shape,  the  more 
the  handle  is  foreshortened. 

Figure  95  represents  the  bottom  of  a  vase,  whose 
actual  form  is  indicated  by  the  light  lines  of  the  section. 
The  lines  of  the  stem  appear  to  end  above  the  centre  of 
the  ellipse,  for  any  conical  form  which  extends  toward 
the  eye  must  have  more  than  half  of  its  surface  visible. 

Figure  96  is  an  elevation  of  a  vase,  the  picture  plane, 
and  the  visual  rays. 

The  rays,  intersecting  the  picture  plane,  give  the  posi- 
tions and  the  lengths  of  the  short  axes  of  the  ellipses 
representing  the  three  plinths,  A,  B,  and  C.  These 
being  drawn,  the  other  lines  of  the  model  drawing.  Fig. 
97,  are  readily  placed. 

The  cuA'ed  lines  of  the  neck  appear  above  to  intersect 
the  lower  ellipse  of  plinth  A,  and  below,  they  end  above 
the  long  axis  of  the  upper  ellipse  plinth  B.  The  body 
of  the  vase  is  represented  by  a  line  tangent  to  or  above 
the  lower  ellipse  of  plinth  B. 

Figure  98  is  an  elevation  of  the  lower  part  of  a  vase 
with  a  spherical  shaped  body  and  a  cylindrical  base 
bavin"  a  curved  moulding. 


126  FKEE-IIAND  DRAWING. 

The  curved  edge  niay  be  drawn  as  the  torus.  The 
body  of  the  vase  is  represented  by  a  line  tangent  to  the 
eHipse  of  the  upper  base  of  the  plinth,  at  points  depend- 
ing upon  the  position  of  the  eye.  When  the  ellipses  are 
narrow,  the  line  will  be  tangent  near  the  ends  of  the 
ellipse,  as  in  Fig.  99. 

When  wider,  the  tangent  points  may  be  near  the  short 
axis  (Fig.  100).  If  still  wider,  the  curve  of  the  body 
appears  a  continuous  line  covering  part  of  the  base  (Fig. 

lOl). 

Figure  102  is  an  elevation  of  a  vase  whose  appearance, 
(to  the  eye  situated  at  the  point  of  convergence  of  the 
visual  rays,)  is  given  by  Fig.  103. 

The  elevation  gives  the  positions  and  lengths  of  the 
short  axes  of  the  ellipses  representing  the  different  circles. 
The  long  axes  are  shorter  than  the  actual  diameters  of 
the  circles,  because  they  are  behind  the  picture  plane. 
The  upper  edge  of  the  vase  is  conical.  The  short, 
straight  lines,  a,  a,  tangent  to  the  two  ellipses,  B 
and  C,  will  be  seen  until  the  larger  ellipse  C  is  wholly 
visible. 

The  student  who  has  a  knowledge  of  Orthographic 
Projection  may  test  his  ability  to  draw  from  a  description 
of  the  form  and  its  position,  by  taking  any  sheets  of  pro- 
jection showing  objects  one  after  another,  supposing  the 
objects  to  be  seen  from  a  certain  point,  and  making 
model  drawings  which  shall  represent  them.     Thus,  Fig. 


PERSPECTIVE  PRINCIPLES.  127 

104  represents  several  objects,  and  their  relations  to  each 
other,  and  the  planes  of  projection. 

Figure  105  is  a  model  drawing  of  the  same,  and  sup- 
poses the  objects  to  be  seen  from  the  left  and  from 
above,  so  that  three  faces  of  the  cube  are  visible. 

The  cube  is  the  first  object,  and  any  drawing  which 
shows  the  top,  front,  and  left  sides,  answers  the  require- 
ments. When  the  cube  is  correct,  the  ground-line  which 
is  parallel  to  the  edges  extending  to  the  right  should  be 
drawn. 

The  cone  is  the  next  object.  Its  base  is  a  circle  of 
the  same  diameter  as  the  base  of  the  cube.  The  best 
way  to  place  the  ellipse,  which  is  the  appearance  of  this 
circle,  is  to  draw  a  square  whose  sides  are  parallel  to 
the  base  of  the  cube.  The  ellipse  must  come  tangent 
to  the  square  at  its  diameters.  The  distance  between  the 
cone  and  the  cube  is  equal  to  half  the  side  of  the  cube.  In 
perspective  this  distance  1-2  will  be  found  by  drawing  the 
diagonals  of  the  right  front  face  of  the  cube.  Setting  off 
this  distance  on  line  AB,  from  2  to  3,  gives  the  nearest 
angle  of  the  square.  Its  sides  extending  to  the  right  are 
continuations  of,  and  are  perspectively  equal  to  those  of 
the  first  square  ;  and  the  sides  extending  to  the  left  are 
parallel  to  those  of  the  first.  It  should  be  remembered 
that  these  lines  continue,  and  vanish  at  right  and  lett  in  a 
horizontal  line  at  the  level  of  the  eye,  and  all  parallel 
lines  should  be  continued   as  far   as   the    drawing   will 


128  FREE-HAND  DRAWING. 

allow,  so  that  they  may  be  given  the  proper  convergence. 
The  student  should  not  attempt  to  have  the  vanishing- 
points  come  on  the  paper.  The  diameters  of  the  base 
give  the  tangent  points  of  the  circle  and  square,  and 
through  them  the  ellipse  must  pass.  The  circle  is  hori- 
zontal, and  the  axis  of  the  ellipse  is  a  horizontal  line. 
The  distance  between  the  centre  of  the  ellipse  and  the 
centre  of  the  square  is  so  slight  as  to  be  hardly  notice- 
able. The  long  axis  of  the  ellipse  is,  however,  in  front 
of  the  centre  of  the  square  ;  and  in  a  larger  drawing, 
where  the  ellipse  is  wide,  if  the  axis  should  be  drawn 
through  the  centre,  the  difference  would  be  very  notice- 
able. The  axis  passes  through  the  centre  of  the  square, 
and  must  be  represented  by  a  vertical  line.  Its  length 
is  readil}'  determined  by  reference  to  the  vertical  edges 
of  the  cijbe,  which  are  half  as  long  as  the  axis. 

The  cylinder  is  next  to  be  considered.  The  nearer 
circle  is  in  the  plane  of  the  front  face  of  the  cube,  and  it 
will  be  best  drawn  by  means  of  the  square  which  circum- 
scribes it.  The  sides  of  the  square  are  parallel  and  equal 
to  those  of  the  right  front  face  of  the  cul)e.  Of  course 
the  distance  5-6  must  be  less  than  3-4,  as  3-4  is  less  than 
0-2,  and  4-5  is  less  than  2-3  (see  Fig.  24).  The 
diagonals  of  the  square  give  its  centre,  and  through  this 
point  the  axis  of  the  cylinder  is  drawn.  The  vertical  and 
horizontal  diameters  give  four  points  in  the  ellipse,  whose 
long  axis  is  a  little  in  front  of  the  centre  of  the  squnre. 


PERSPECTIVE  PRINCIPLES.  129 

and  at  right  angles  to  the  axis  of  the  cyHnder.  In  the 
same  way,  the  farther  end  may  be  drawn.  The  length  of 
the  cylinder  being  twice  the  side  of  the  cube,  the  dis- 
tance 7-8  is  perspectively  equal  to  5-7. 

The  hexagonal  prism  is  the  last  object.  It  is  vertical, 
with  one  face  in  the  plane  of  line  AB.  A  diagonal  of 
its  base  is  parallel  to  .AB.  Its  length  may  be  placed  on 
AB,  from  9  to  10,  perspectively  equal  to  5-6,  the  dis- 
tance 6-9  being  perspectively  equal  to  4-5.  Points  11, 
12,  and  13,  (dividing  9-10  into  four  perspectively  equal 
parts,)  being  placed,  the  diameters  of  the  hexagon  extend 
from  IT  and  13  toward  the  left-hand  vanishing-point. 
The  side  14-15  having  been  drawn,  the  diagonals  11-15 
and  13-14  give  the  centre  of  the  hexagon.  Through 
this  point  the  diagonal  parallel  to  11-13  passes,  and  the 
lines  from  9  and  10  place  in  it  the  two  remaining  angles 
of  the  base,  16  and  17.  The  left  vertical  face  A  appears 
narrowest.  This  shows  that  16  is  nearer  than  13,  and 
the  diameter  16-13  inclines  upward  slightly  from  16. 

These  drawings  call  for  lines  at  definite  angles  with  the 
ground  and  the  vertical  plane.  Such  angles  may  be  de- 
termined by  means  of  the  cube,  and  for  this  reason  it 
will  be  well  to  draw  this  object  first,  even  when  it  is  not 
called  for. 

The  edges  of  the  cube.  Fig.  106,  being  perpendicular 
to  the  two  planes,  the  diagonals  of  its  faces  are  at  45°. 
If  smaller  angles  are  desired,  they  can  be  obtained  by 


130  FREE-HAND  DRAWING. 

subdividing  the  angles  of  45°.  In  making  this  division, 
it  must  be  noticed  that  equal  angles  never  appear  equal 
when  occupying  different  positions  with  regard  to  the  pic- 
ture plane. 

Figure  107  shows  that  equal  angles  appear  unequal, 
and  larger,  the  more  the  lines  of  the  angles  are  foreshort- 
ened, so  that  to  divide  Any  angle,  the  part  which  is  most 
foreshortened  must  be  represented  by  the  greater  angle, 
and  as  equal  angles  approach  the  position  in  which  they 
are  "  not  foreshortened,"  they  will  appear  smaller. 

By  holding  a  triangular  card,  the  student  will  see  that 
an  angle  less  than  90°  may  appear  greater  than  90°, 
when  its  sides  are  much  foreshortened.  In  fact,  the  small- 
est angle  may  appear  any  angle  up  to  180°.  An  angle 
greater  than  90°  may  in  the  same  way  appear  any  size 
up  to  180°. 

When  the  plane  of  the  angle  is  foreshortened  more  than 
the  sides  of  the  angle,  the  angle  appears  less  than  its  real 
size,  and  any  angle  may  appear  the  smallest  possible  to 
be  measured.  //  is  thus  seen  that  an  angle  may  appear 
any  angle  from  the  smallest  up  to  180° 

Such  practice  will  more  quickly  than  any  other  work 
show  the  student  whether  he  really  understands  the  prin- 
ciples, or  has  been  merely  memorizing  tliem.  The  latter, 
which  unfortunately  is  the  only  way  many  study,  will  be 
found  entirely  useless,  and  those  who  have  been  working 
thus,  must  start  again  with  the  determination  to  see  with 


PERSPECTIVE  PRINCIPLES.  131 

their  own  eyes,  and  to  accept  nothing  which  they  have 
not  verified  by  careful  study. 

The  principles  which  have  been  explained  enable  one 
to  see  as  it  is  impossible  to  see  without  them,  to  draw 
without  the  objects,  to  draw  from  memory,  and  to  design 
geometric  forms  of  any  size  and  in  any  position.  They 
are  of  so  much  value  to  the  practical  draughtsman  that 
he  cannot  afford  to  be  without  them,  even  were  it  very 
difficult  to  obtain  this  knowledge.  The  principles  are, 
however,  so  simple  that  there  is  no  excuse  for  violations 
of  the  few  essential  ones ;  yet  such  violations  are  found 
very  frequently,  not  only  in  the  work  of  the  amateur,  but 
also  in  that  of  the  professional  draughtsman. 

Although  the  principles  must  be  carried  out  in  all  good 
drawings,  theory  alone  should  be  depended  upon  only 
when  designing  or  drawing  imaginary  subjects.  When 
Nature  can  be  studied,  the  rules  may  be  applied  after 
careful  consideration  of  the  appearances,  and  it  is  not 
intended  or  supposed  that  the  principles  will  render  this 
study  of  Nature  unnecessary.  When  understood,  they 
are  of  most  value  in  assisting  the  mind  to  accept  the 
image  of  the  eye,  and  are  unconsciously  applied. 

Review  of  Important  Principles. 

Any  line  whose  ends  are  equally  distant  from  the  eye 
appears  its  real  length.  Any  plane  whose  angles  are 
equally  distant  appears  its  real  shape. 


132  FREE-HAND  DRAWING. 

2.      Parallel,  retreating  lines  appear  to  converge,  or  vanish 
toward  a  point  called  their  vanishing-point. 
^         Of  two  parallel  and  equal  lines  which  do  not  vanish, 

the  nearer  appears  the  longer. 
tJ.       Equal  spaces  on  any  retreating  line  appear  unequal, 

the  nearest  appearing  the  longest. 
^      All  lines  whose  ends  are  unequally  distant  from  the  eye 

are  lines  which  appear  to  vanish. 
^       Horizontal,  retreating  lines,  above  the  eye,  appear  to 

descend,  or  vanish  downward. 
Y      Horizontal,  retreating  lines,  below  the  eye,  aj)pear  to 

ascend,  or  vanish  upward. 
y       Parallel,  retreating   horizontal  lines  appear   to  vanish 

at  the  level  of  the  eye. 
^         A  horizontal  line  at  the  level  of  the  eye  appears  hori- 
zontal, and  a  horizontal  plane  at  this  level  appears  a  liori- 
zontal  line. 
/(J        The  vanishing-point  of  any  set  of  parallel  lines  is  in  a 
parallel  to  them  passing  through  the  eye.     Hence,  to  see 
the  vanishing-point  of  any  lines,  we  must  look  in  their 
direction. 
r.        Of  two  parallel  and  equal  lines  which  are  foreshortened, 
the  nearer  may  appear  the  shorter. 
/^       Of  two  equal  lines  which  are  perpendicular  to  each 
other  and  have  one  end  common,  the  one  at  the  greater 
angle  with  the  picture  plane   appears  the  shorter,  and 
vanishes  at  the  greater  angle. 


PERSPECTIVE  PRINCIPLES.  133 

^"^      If  one  side  of  a  square  vanishes  toward  the  left,  the 

other  side  vanishes  toward  the  right. 
/^      When  the  sides  of  a  square  make  equal  angles   with 
the  picture  plane,  they  appear  of  equal  lengths,  and  the 
*'  angles  of  inclination  and  convergence  "  are  equal. 
yf       The    "  angle    of   inclination "  of   any   retreating    line 
depends  upon  the  level  of  the  eye  and  its  distance  from 
the  line,  but  it  is  always  much  less  than  the  real  angle 
that  the  line  makes  with  the  picture. 
/6        The  convergence  of  parallel  lines  is  in  the  direction  of 
their  fiirther  ends.      These  are  points   of  the  invisible 
faces  of  any  right  square  prism. 
jY       If  both  ends  of  any  edge  are  points  of  invisible  faces, 
the  edge  must  be  considered   as  "  not  foreshortened," 
even  if  its  ends  are  unequally  distant  from  the  eye. 

Straight  lines  must  generally  be  represented  by  straight 
hnes,  and  vertical  lines  by  verticals. 

If  two  of  the  vertical  sides  of  a  cube  or  prism  are  seen, 
both  sets  of  horizontal  lines  appear  to  converge. 

When  one  diagonal  of  a  horizontal  square  appears  a 
vertical  line,  the  other  appears  a  horizontal  line,  and  the 
sides  vanish  equally  in  each  direction. 
fl2»  I         Wlien  the  pyramid  is  vertical,  its  vertex  is  in  a  vertical 

line  through  the  centre  of  the  base. 
Uj  *^        The  vertex  of  an  isosceles  or  equilateral  triangle  is  in 

a  perpendicular  to  the  base  at  its  centre. 
Q^  ^        The  diameters  and  diagonals  of  the  regular  hexagon 


134  FREE-HAXD  DRAWING. 

divide  the  diagonal  which  they  intersect  into  four  equal 

parts. 
2,^       The  circle  generally  appears  a  circle,  a  straight  line,  or 

an  ellipse. 
JIS"      A  horizontal  circle,  above  or  below  the  level  of  the  eye, 

appears  a  horizontal  ellipse. 
5  f         The  centre  of  the  circle  does  not  appear  the  centre  of 

the    ellipse,  and   the  long  axis  of  the  ellipse   is   not   a 

diameter  of  the  circle, 
or         The  foreshortened  vertical  circle,  when  above  or  below 
'         the  level  of  the  eye,  appears  an  ellipse  whose  long  axis 

is  not  a  vertical  line. 
2  ^        The  long  axis  of  the  ellipse  appears  perpendicular  to 

a  line  which  is  at  right  angles  to  the  circle  at  its  centre. 
9  ^         Only  one  end  of  a  cylinder  can  appear  a  straight  line 

at  one  time.     The  other  end  appears  an  ellipse. 
3d  If  any  of  the  curved  surface  of  the  cylinder  with  an 

end  is  seen,  the  end  does  not  appear  a  circle. 
0/  If  the  visible  end  appears  an  ellipse,  the  invisible  end 

appears  an  ellipse  proportionally  wider  than  the  visible 

end. 
<^*^        The  long  axes  of  the  ellipses  are  perpendicular  to  the 

axis  of  the  cylinder. 
^  3         Any  part  of  the  convex  surface  of  the  cone  may  be 

seen  at  one  time.     When  the  cone  is  vertical  and  below 

the  eye,  more  than  half  is  visible ;  when  above  the  eye, 

less  than  half. 


PERSPECTIVE  PRIXCTPLES.  135 

^f-      When  the  base  appears  an  ellipse,  its  long  axis  appears 
perpendicular  to  the  axis  of  the  cone. 

7^  The  contour  elements  of  the  cylinder  and  cone  appear 
tangent  to  the  ellipses  of  the  bases.  In  the  cylinder, 
the  tangent  points  are  frequently  not  in  the  axis  of  the 
ellijise.  In  the  cone,  they  are  never  in  the  axis. 
5/  The  apparent  distance,  measured  on  the  short  axis, 
between  the  ellipses  representing  concentric  circles  is 
the  same  perspective  part  of  the  short  axis  that  the  dis- 
tance between  the  ellipses,  measured  on  the  long  axis,  is 
of  the  entire  long  axis. 

^^        The   lines   which   represent   a    foreshortened   vertical 
*       ring  are  nearly  parallel  to  an  ellipse  which  represents  its 
centre  line.     They  are  not  eUipses. 

a  ^        The  angles  of  two  polygons,  whose  centres  coincide, 
and  whose  sides  are  parallel,  are  in  the  same  diagonal 
lines. 
■^Q  An    angle    may   appear  of  any  size,   large   or   small, 

'        according  to  whether  the  sides  or  the  plane  of  the  sides 
is  foreshortened. 

The  above  are  most  of  the  points  essential  to  the  draughtsman; 
and  those  not  teachers,  and  those  unable  to  follow  all  the  chapter, 
and  those  not  interested  in  the  subject  for  itself,  may  find  that  the 
review  includes  nearly  all  that  they  need. 


CHAPTER  VII. 
Questions  for  Ex.\minations. 

To  he  answered  by  drawings,  supplemented,  if  necessary,  by  writing. 
Unless  otherwise  stated,  all  drawings  are  to  be  Model  Drawings. 

1.  Illustrate  by  diagrams  representing  the  eye,  the 
picture  plane,  and  a  sphere,  the  different  positions  of 
the  picture  plane  which  produce  "  true  "  and  distorted 
pictures. 

2.  How  do  parallel  retreating  lines  appear?  Illus- 
trate by  a  cube  all  of  whose  lines  appear  to  converge. 
Show  by  arrows  the  directions  in  which  the  lines  vanish. 

3.  Illustrate  by  sketch  of  a  cube  the  way  parallel, 
retreating  horizontal  lines  appear. 

4.  Represent  a  horizontal  square  plane,  whose  sides 
extend  to  the  left  at  30°,  and  to  the  right  at  60°,  when 
the  plane  is  on  the  level  of  the  eye. 

5.  In  any  background,  how  is  the  position  found  of 
the  point  where  parallel  lines  appear  to  vanish?  Illus- 
trate by  sketch  of  any  room,  with  a  box  upon  the  floor, 
and  write  any  points  which  the  sketch  may  not  make  clear. 

6.  How  do  vertical  lines  above  the  eye  appear,  and 
how  should  they  be  represented  ?  Illustrate  by  sketches 
of  a  cube. 

136 


QUESTIONS  FOR  EXAMTNATtONS.  137 

7.  Make  a  sketch  of  a  cylinder  or  a  square  prism, 
which  shall  show  that  the  more  distant  of  two  parallel 
and  equal  lines  may  appear  the  longer.  Mark  the 
nearer  line  AB,  the  farther  CD. 

8.  The  "  angles  of  inclination "  of  the  lower  visible 
edges  of  a  cube  which  is  below  the  eye,  and  rests  on  a 
face  on  the  floor  are  equal.     Represent  the  cube. 

9.  How  do  parallel  straight  lines  in  Nature  appear? 
Illustrate  by  representing  the  actual  appearance  of  each 
of  three  cubes,  placed  first,  in  a  straight  line  upon  the 
floor ;  second,  in  a  vertical  line,  one  being  on  the  floor, 
another  on  the  level  of  the  eye,  and  the  last  above  this 
level. 

10.  By  sketches  of  the  three  cubes  in  the  above 
positions,  show  how  straight  lines  should  generally  be 
represented. 

1 1 .  Give  the  actual  appearance  of  a  horizontal  cylin- 
der whose  length  is  2,  diameter  i,^  when  below  the  eye, 
and  so  placed  that  the  left-hand  base  appears  a  vertical 
line. 

12.  Show  by  a  sketch  of  an  interior  when  this  appear- 
ance would  be  the  best  drawing  of  the  cylinder. 

13.  As  a  representation  of  simply  the  cylinder,  what 
drawing  is  better  than  the  actual  appearance  ? 

14.  Represent  a  cube  above  the  eye,  with  four  edges 
vertical,  when  three  of  its  sides  are  visible  as  surfaces. 

1  The  cylinder  may  be  drawn  of  any  size  but  of  these  proportions, 
and  the  same  for  following  problems. 


138  FREE-HAND  DRAWING. 

15.  The  same  cube  when  a  diagonal  of  its  visible 
horizontal  face  appears  a  vertical  line ;  and  a  vertical 
square  prism,  whose  length  is  3,  diameter  i,  having  upon 
it  a  square  pyramid  whose  base  is  2,  axis  2.  The  axes 
of  the  solids  coincide,  and  the  edges  of  the  bases  are 
parallel.     The  lower  base  of  prism  on  level  of  eye. 

1 6.  Above  solids  when  the  eye  is  on  the  level  of  the 
centre  of  the  prism,  and  a  face  of  this  object  is  "not 
foreshortened." 

17.  The  same  solids  and  conditions,  except  that  two 
faces  of  the  prism  arc  seen  equally. 

18.  A  prism  whose  ends  are  equilateral  triangles 
whose  sides  are  half  as  long  as  the  prism,  rests  upon 
a  face  upon  the  floor  below  the  eye.  The  sides  of  the 
face  on  the  ground  extend  to  right  and  left  at  equal 
angles  with  the  picture.  The  left  base  is  visible.  Show 
all  tests  of  the  drawing,  and  the  directions  in  which  all 
the  lines  vanish. 

19.  The  same  when  the  object  is  above  the  eye. 

20.  The  same  object  when  above  the  eye,  and  the 
ends  of  its  horizontal  face  are  "  not  foreshortened." 

21.  A  regular  hexagonal  card,  horizontal  and  above 
the  eye,  with  one  diagonal  "  not  foreshortened." 

22.  The  same  card  vertical  and  on  the  level  of  the 
eye,  and  vanishing  to  the  right.  Its  diameters  are  ''  not 
foreshortened." 

23.  The  prism  shown  in  Fig.  55,  when  it  is  horizontal 
and  above  the  eye. 


QUESTIONS  FOR   EXAMINATIONS.  139 

24.  The  same  when  it  is  below  the  eye,  and  horizon- 
tal, with  its  long  edges  "not  foreshortened." 

25.  The  pyramid  of  Fig.  56  when  it  is  above  the  eye, 
with  the  diameters  of  its  base  "not  foreshortened." 

26.  Place  under  the  pyramid  (Fig.  56)  a  cube,  one 
diagonal  of  its  top  coinciding  with  the  marked  diagonal 
of  the  base  of  the  pyramid.  The  square  is  to  be  larger 
than  the  hexagon. 

27.  Represent  when  below  the  eye  a  horizontal  hex- 
agonal plinth,  a  square  pyramid  placed  upon  its  top,  and 
a  hexagonal  pyramid  resting  obliquely  upon  the  floor 
and  the  plinth. 

28.  A  cube  with  inscribed  circles  tangent  to  each 
square,  when  below  the  eye  with  first,  two  surfaces 
visible  ;  and  second,  three  surfaces  visible. 

29.  Show  by  a  horizontal  circle  above  the  eye  that 
the  centre  of  the  circle  is  not  represented  by  the  centre 
of  the  ellipse. 

30.  The  long  axis  of  the  ellipse  is  what  line  of  the 
circle  ? 

31.  How  do  equal  spaces  on  any  retreating  line 
appear?     Illustrate  by  an  "elevation," 

32.  A  horizontal  circle  is  seen  by  several  persons  who 
are  the  same  distance  above,  and  away  from  the  circle. 
Does  the  same  line  of  the  circle  appear  to  the  different 
observers  the  long  axis  of  the  ellipse?  Illustrate  by  a 
"  plan." 


140  FREE-HAND   DRAWING. 

33.  Sketch  a  spinning-wheel  which  is  below  the  level 
of  the  eye. 

34.  A  vertical  cylinder  whose  visible  end  is  above  the 
level  of  the  eye. 

35.  A  horizontal  cylinder  on  the  level  of  the  eye,  the 
cylinder  "  not  foreshortened." 

36.  Why  do  not  the  long  axes  of  the  ellipses  in  Fig. 
68  vanish? 

37.  Represent  a  horizontal  retreating  cylinder  above 
the  level  of  the  eye,  and  so  situated  that  its  axis  appears 
a  vertical  line. 

38.  A  parallel  cylinder  on  the  same  level  and  to  the 
right  of  the  last  object,  the  ends  of  the  cylinders  in  the 
same  planes. 

39.  The  retreating  vertical  side  of  a  building  which 
has  in  it  three  semicircular  arches  in  the  same  vertical 
line,  the  eye  on  the  level  of  the  centre  of  the  central 
arch.     (See  Fig.  64.) 

40.  A  vertical  cylinder,  diameter  i,  length  2,  with  a 
cone  upon  it,  the  bases  coinciding ;  eye  on  level  of  the 
centre  of  the  cylinder. 

41.  A  horizontal  circle  is  represented  by  an  ellipse, 
whose  long  axis  is  4|"  long,  whose  short  is  i|^"  long.  A 
concentric  smaller  circle  appears  an  ellipse  which  inter- 
sects the  long  axis  of  the  outer  at  points  |^"  from  its 
ends. 

42.  Represent  a  horizontal  retreating  pipe  below  the 


QUESTIONS  FOR   EXAMINATIONS.  141 

level  of  the  eye      Its  inner  diameter  half  of  its  outside 
diameter. 

43.  A  horizontal  cylinder,  diameter  i,  length  2,  its 
axis  on  the  level  of  the  eye,  and  extending  to  the  right 
at  an  angle  of  45°  with  the  picture,  and  a  second  equal 
cylinder  just  below,  its  ends  in  the  same  planes  as  those 
of  the  upper. 

44.  A  vertical  cone,  resting  upon  the  centre  of  a 
horizontal  stjuare  plinth  whose  vertical  sides  are  seen 
unequally,  and  a  circular  ring  square  in  section,  resting 
obliquely  against  the  plinth. 

45.  The  pyramid  of  P'ig.  77  when  above  the  level  of 
the  eye. 

46.  The  same  for  the  cone  of  Fig.  80, 

47.  A  conical  pail,  of  which  the  curved  outer  surface 
with  the  inner  surface  of  the  bottom  is  visible. 

48.  A  cuspidore  of  double  cone  form  when  below  the 
eye. 

49.  The  double  cone  of  Fig.  83  when  it  is  horizontal, 
below  the  eye,  and  at  a  large  angle  with  the  picture 
plane. 

50.  The  ring  of  Fig.  85  when  it  is  vertical,  and  on 
the  level  of  the  eye,  and  more  foreshortened  than  in  the 
figure. 

51.  The  frame  of  Fig.  88  when  the  axis  of  the  ellipse 
representing  the  tangent  circle  is  pa.rallel  to  a  side,  as  B. 

52.  The  same  when  the  axis  is  parallel  to  a  diagonal 
of  the  square. 


142  FREE-HAND  DRAWING. 

53.  A  triangular  frame  when  it  is  horizontal  and 
below  the  eye,  with  the  most  distant  sides  of  the  trian- 
gles "  not  foreshortened." 

54.  A  vertical,  foreshortened  hexagonal  frame  below 
the  eye. 

55.  A  table  with  a  square  top  and  inclined  legs. 

56.  A  vertical  cylinder  below  the  eye,  with  a  mould- 
ing half  round  in  section  at  the  top,  one  square  in  sec- 
tion at  the  bottom,  and  a  groove  square  in  section  cut 
in  the  centre  of  the  cylinder.  Diameter  of  cylinder  i, 
length  2.     Width  of  bands  \. 

57.  The  vase  of  Fig.  92  when  seen  from  below. 

58.  The  same  when  seen  from  above,  and  very  near 
so  that  the  ellipses  are  wide. 

59.  The  vase  of  Fig.  96  when  the  bottom  is  visible. 
Og.   The  same  for  Fig.  98. 

61.  The  same  for  Fig.  102. 

62.  Sketch  an  interior  representing  the  floor  and  two 
walls,  with  a  table  or  other  objects. 

63.  The  same,  showing  in  addition  the  ceiling,  or 
horizontal  objects  above  the  eye. 

64.  Sketch  an  interior  representing  three  walls  and 
furniture. 

65.  An  interior  representing  one  wall,  with  objects 
parallel  to  the  wall,  and  on  each  side  of  the  spectator. 

66.  The  same  when  spectator  is  near  an  end  of  the 
wall. 


QUESTIONS  FOR  EXAMINATIONS.  143 

The  following  questions  are  for  those  who  understand 
Orthographic  Projection  and  Scientific  Perspection.' 

67.  Illustrate  the  difference  in  appearance  between  a 
perspective  drawing  of  a  cube  placed  at  the  left,  below 
the  eye,  and  with  one  face  parallel  to  the  picture  plane, 
and  a  model  drawing  of  the  same. 

68.  The  same  for  a  cone  at  the  right  and  vertical. 

69.  The  same  for  a  horizontal  cylinder  parallel  to  the 
picture  plane,  and  its  right  base  visible. 

70.  Make  a  perspective  drawing  of  a  horizontal  square, 
which  shall  show  that  the  perspective  of  a  retreating  line 
may  be  longer  than  the  line.  Make  a  model  drawing  of 
the  same  square. 

71.  Illustrate  by  means  of  the  perspectives  of  a  sphere 
the  distortion  found  in  a  Plane  Perspective  representing 
objects  above,  below,  or  to  the  left  or  the  right  of  the 
point  opposite  the  eye.  State  briefly  the  diflerence 
between  a  Perspective  and  a  Model  Drawing. 

72.  Represent  the  objects  shown  by  Figs.  104  and 
105  when  they  are  seen  from  the  right  instead  of  from 
the  left. 

1  An  illustrated  pamphlet  comparing  Plane  Perspective  and  Model 
Drawing  will  be  mailed  on  receipt  of  fifteen  cents,  to  those  teachers  who 
wish  more  on  this  subject  than  this  book  contains. 


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SUGGESTIONS  FOR  FIRST  LESSONS  IN  THE  PUBLIC  SCHOOLS. 

[These  objects  and  similar  ones  should  be  studied  in  different  positions  until  they  can  be  well  and  easily  drawn.] 


Square  Card. 


Circular  Card. 


Square  Card. 


Triangular  Card. 


Square  Card. 


L 


\ 


Rectangular  Card. 


Rectangular  Card. 


Rectangular  Ca'd. 


Triangular  Card. 


Hexagonal   Card. 


Hexagonal  Card. 


Triangular  Card. 


Horizonia!  and  Vertical  Squares. 


L 


Horizontal  Squares. 


Vertical  Squares. 


Horizontal  Circles. 


Vertical  Triangles. 


THE  LIBRARY 
UNIVERSITY  OF  CALIFORNIA 

Santa  Barbara 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW. 


MAY  3    1989 


hZTTMYi    ^^^^B 


Series  9482 


^ 


[;C  SOU'^HEaN  REGIONAL  LIBRARY  FACILJTY 


A     000  647  340     9 


